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  • 1
    Electronic Resource
    Electronic Resource
    Editorial (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
    Details
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00468.x
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  • 2
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    Families, Children and Probabilities (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00469.x
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  • 3
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    Electronic Resource
    What's in the Package? Sample and See! (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00470.x
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  • 4
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    A Class Exercise Concerning the Distribution of Plants (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00471.x
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  • 5
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    The Pie Chart: A Piece of Cake (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00472.x
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  • 6
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    Letters (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00476.x
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  • 7
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    Statistics on a Circle (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00475.x
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  • 8
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    Putting the Shoe on the Other Foot (1982)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: An example of the use of an induction proof in elementary probability theory and its application in proving a theorem in number theory.
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  • 9
    Electronic Resource
    Electronic Resource
    On an Awareness of Alternative Approaches to Index Numbers (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 10
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    News and Notes (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00478.x
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  • 11
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    Book Reviews (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Introductory Statistics: Volume 1, Probability and Distribution TheoryWorked Examples in Probability and Distribution Theory.Elementary Statistics Tables. By Henry R. Neave.Ideas of Statistics. By J. Leroy Folks.Advanced Mathematics Book 1. By M. Perkins and P. Perkins.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
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    Editorial (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00456.x
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  • 13
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    Probability and The F.A. Cup (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00457.x
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  • 14
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    Height, Weight, Expectation and Variance (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00458.x
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  • 15
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    Do-it-yourself Opinion-poll Sampling Experiments (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00459.x
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  • 16
    Electronic Resource
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    Balancing a Skew Distribution (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00461.x
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  • 17
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    Neat Data for Teaching Statistics (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00460.x
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  • 18
    Electronic Resource
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    An Area Approach to Probability (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 19
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    Exploring a Random Sampling Method used in Biology (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00463.x
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  • 20
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    What's in the Package—On Average? (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00464.x
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  • 21
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    Do Men have more Sisters than Women? (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 22
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    Letters (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 23
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    News and Notes (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 24
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    Editorial (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 25
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    The Role of Practicals in Statistics (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00444.x
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  • 26
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    A Stimulating Simulation (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00446.x
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  • 27
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    Statistics and Probability before the age of 15 at Decroly School (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Statistics is not usually taught to pupils below 15 years old in the majority of secondary schools in Belgium. One school does include it in its curriculum for such pupils und this article outlines the reasons and methods involved.
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  • 28
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    The Birthday Problem: Some Empirical Data and Some Approximations (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 29
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    Probability: A Project Approach (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 30
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    Areas Under the Regression Curves (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 31
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    Australia-England Test Cricket (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 32
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    Interpreting Statistical Significance (1982)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 33
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    An Unusual Weekend for Second Division Football (1982)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 4 (1982), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 34
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    Letters (1982)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1982.tb00454.x
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  • 35
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    Book Reviews (1982)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Advanced Level Statistics. By A. Francis.Studying Society. By Jane L. ThompsonElementary Statistics for Business. By J. S. CroucherStatistics: An Introduction. By J. S. Croucher and E. OliverBasic Business Statistics. Concepts and Applications. By M. L. Berenson and D. M. Levine.
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  • 36
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    News and Notes (1982)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 37
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    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
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  • 38
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    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
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    URL: http://dx.doi.org/10.1007/BF02459417
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  • 39
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    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
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  • 40
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    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
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    URL: http://dx.doi.org/10.1007/BF02459420
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  • 41
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    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
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    URL: http://dx.doi.org/10.1007/BF02459419
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  • 42
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    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
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    URL: http://dx.doi.org/10.1007/BF02459421
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  • 43
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    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
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    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 149-150 
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    Transient effects on the initial rate of oxygenation of red blood cells (1982)
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    Bulletin of mathematical biology 44 (1982), S. 119-134 
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    Notes: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
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    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
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    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    Notes: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
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    A stochstic model for a two-compartment reversible system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    Notes: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
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    Effects of dispersion on stability of multispecies prey-predator systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 571-578 
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    Notes: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
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    Repeatability of experiments (1982)
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    Bulletin of mathematical biology 44 (1982), S. 593-593 
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    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 579-585 
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    Notes: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
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    A reply to “repeatability of experiments” by R. B. Campbell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 594-595 
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    An epizootic model of an insect-fungal pathogen system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 731-739 
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    Notes: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
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    On feedback control of gonadotropin secretion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 741-748 
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    Notes: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
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    The development of largangians for biological models (1982)
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    Bulletin of mathematical biology 44 (1982), S. 749-760 
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    Notes: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
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    An optimal control model of diabetes mellitus (1982)
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    Bulletin of mathematical biology 44 (1982), S. 793-808 
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    Notes: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
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    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 777-791 
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    Notes: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
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    The development of anoxia following occlusion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 851-877 
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    Notes: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 899-900 
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    Selection under random mutations in stochastic eigen model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 17-28 
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    Notes: Abstract The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.
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    Factors defining the rate of oxygen uptake by the red blood cell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 135-147 
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    Notes: Abstract Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.
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    Book review (1982)
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    Bulletin of mathematical biology 44 (1982), S. 151-151 
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic Ganglia (1982)
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    Bulletin of mathematical biology 44 (1982), S. 152-152 
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    On a class of finite deformations of elastic soft tissues (1982)
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    Bulletin of mathematical biology 44 (1982), S. 175-192 
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    Notes: Abstract Due to the complicated physiological structure of soft biological tissues, stresses can only be measured after the specimen has been stretched to many times of its related length. Therefore, the classical constitutive equations of finite elasticity developed for vulcanized, rubbery materials and the linear theories developed for most engineering materials cannot be applied to soft tissues which are highly elastic in nature. In this article, utilizing a mechanical model developed by Demiray for soft tissues, a class of finite deformations of some tissues is studied and the results are compared with experiment and the existing literature. These problems are the simultaneous extension and twisting of a circular cylindrical bar, the bending of a rectangular block, and the pure shear of a rectangular prism. It is believed that solutions to these problems may find some applications in plastic surgery.
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    Effects of convective and dispersive migration on the linear stability of a two species system with mutualistic interactions and functional response (1982)
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    Bulletin of mathematical biology 44 (1982), S. 271-282 
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    Notes: Abstract In this paper, effects of convective and dispersive migration on the linear stability of the equilibrium state of a two species system with mutualistic interactions and functional response have been investigated. In both finite and semi-infinite habitats, it has been shown that the otherwise stable equilibrium state without dispersal remains so with dispersal also, both under flux and reservior conditions. In the case of finite habitat, the degree of stability increases as dispersal coefficients of the two species increase. The effect of convective migration also is to stabilize the equilibrium state in this case.
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    Bulletin of mathematical biology 44 (1982), S. 307-307 
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    A model of the spatial-temporal characteristics of the alpha rhythm (1982)
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    Bulletin of mathematical biology 44 (1982), S. 283-305 
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    Notes: Abstract A linear spatially distributed model of a chain of neurons and interneurons was investigated in relation to the generation of propagated alpha rhythmic activity. It was assumed that the elements of the chain were interconnected by means of recurrent collaterals and inhibitory fibres in such a way that the connectivity functions were assumed to be homogeneous and their strength was an exponentially decreasing function of distance. It was found that such a neuronal chain shows propagation properties for frequencies in the alpha band. The results obtained with the model are in agreement with the phase velocities encountered experimentally. In this way, it was possible to estimate the length of the neural fibres responsible for the phenomenon of propagated activity. The estimates obtained are in good agreement with recent quantitative neuroanatomical data on the circuitry of the neocortex.
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    A behavioral summary for completely random nets (1982)
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    Bulletin of mathematical biology 44 (1982), S. 309-320 
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    Notes: Abstract This paper characterizes the cycle structure of a completely random net. Variables such as number of cycles of a specified length, number of cycles, number of cyclic states and length of cycle are studied. A square array of indicator variables enables conveninent study of moment structure. Additionally, exact and asymptotic distributional results are presented.
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    Eigensolutions of nonlinear wave equations in one dimension (1982)
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    Bulletin of mathematical biology 44 (1982), S. 321-337 
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    Notes: Abstract A class of nonlinear equations describing the steady propagation of a disturbance on the infinite interval in one dimensional space are shown under certain conditions to admit solution with a unique velocity of propagation. The class of equations describe both initial and final homogeneous steady states which are asymptotically stable with respect to uniform perturbations, in contrast to the Fisher equation, which does not.
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    Comparison of models of insulin release (1982)
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    Bulletin of mathematical biology 44 (1982), S. 399-409 
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    Notes: Abstract A model for insulin secretion with a storage and a labile compartment, as well as a provisionary factor, is combined with a signal model in which the signal can be the difference between an excitation and an inhibition, or the difference in concentrations inside and outside some cell components. The model, using a single set of values for the parameters, accounts in a semiquantitative manner for all of the regularly appearing features of the insulin secretion from thein vitro perfused pancreas to a wide range of patterns of glucose and tolbutamide stimulation. Among the features which can be accounted for are: early and late secretion of insulin as a function of glucose in terms of a single parameter; the apparent depletion and recovery during a pulsed pattern of stimulation by tolbutamide; the hypersecretion following a short period of rest during a prolonged stimulation by glucose; the negative spike which occurs when the concentration of glucose, which has been maintained for a period of time, is suddenly reduced to a lower level; and the appropriate responses to slow and fast ramp functions of glucose concentration.
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    Example of a system which is computation universal but not effectively programmable (1982)
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    Bulletin of mathematical biology 44 (1982), S. 443-447 
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    Notes: Abstract The incorporation of a chaotic component in a computing system is incompatible with its being effectively programmable. The example presented shows that concepts of programming suitable for biological systems may differ from those which have grown out of our experience with present day digital computers.
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    Primary events in odour detection (1982)
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    Bulletin of mathematical biology 44 (1982), S. 411-423 
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    Notes: Abstract An analysis of the interaction between stimulus molecules and the olfactory receptor cell membrane is presented. The model is based upon a sequence of events, i.e. stimulus delivery at the olfactory epithelium, absorption of molecules in the mucus layer, diffusion of the molecules towards the receptor cells and molecule-receptor cell membrane interaction. The mathematical analysis considers the situation during electrophysiological experiments, where an odour puff is delivered at an exposed olfactory mucosa. Such a situation resembles sniffing of odour samples. The analysis is discussed in relation to experimental evidence.
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    Analytical model of hygroscopic particle behavior in human airways (1982)
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    Bulletin of mathematical biology 44 (1982), S. 425-442 
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    Notes: Abstract A model is developed to calculate the deposition of hygroscopic aerosols in the human tracheobronchial (TB) tree. The TB airflow pattern assumed is consistent with experimental observations and accounts for anatomical features such as the larynx and cartilaginous rings in large airways. Some original deposition efficiency formulae are presented for laminar and turbulent airstreams. Stepwise growth is simulated by changes in particle size and density at each TB generation. The dose distribution of NaCl aerosols is studied as a function of inhaled particle size and flow rate. Two NaCl growth rate curves are used which differ in the mode of aerosol-air mixing in the trachea. The initial rate of aerosol mixing in the human due to the laryngeal jet is shown to be an important factor affecting the deposition of hygroscopic aerosols. Total TB deposition of NaCl exceeds that for nonhygroscopic particles of the same inhaled aerodynamic size. Hygroscopic growth can also influence the regional TB distribution of dose when submicron NaCl particles grow rapidly enough to deposit by impaction and sedimentation.
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    Remark on the letter by Zhitomirsky and Kagna (1980) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 449-449 
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    Bulletin of mathematical biology 44 (1982), S. 451-452 
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    Mathematical model for the study of fertility and viability in inbreeding populations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 491-500 
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    Notes: Abstract Granted that a single or complex gene is responsible for inbreeding depression, theoretical expressions for fertility and viability are obtained in different diploid populations: brother-sister, half-brother-sister, cousins and double-cousins. The conclusions of the study of viability variations according to the coefficient of parentage are proved by the results of experiments and lead to a new view of genetic load.
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    Energy and biological evolution—I. The equilibrium states of biochemical processes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 501-535 
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    Notes: Abstract The Thom gradient model of morphogenesis poses the followinga posteriori problem: “From the observed morphology of a given natural process (effect) determine the dynamics of the process (cause)”. In this paper we consider the classicala priori problem: “Given the cause (dynamics) determine the effect (resultant morphology)”. We find that in biochemical processes the mechanisms for energy activation, energy-matter interaction and energy dissipation determine the dynamics. Furthermore there exists basic energy mechanisms which drive the equilibrium states through the elementary catastrophes of Thom. A comparison with current theories shows that our models describe open ecological food chains and their dynamical systems generalize the equations of organisation posed by M. Eigen.
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    Energy and biological evolution—III. Theoretical ecology and macromolecular self-organization (1982)
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    Bulletin of mathematical biology 44 (1982), S. 549-555 
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    Notes: Abstract We show that the elementary models of biochemical evolutionary processes are the bases for the study of open ecological systems and macromolecular self-organisation. We deduce a biochemical analogue for the basic closed phytoplankton-zooplankton food chain. The perturbation of the Michaelis-Menten mechanism which determines the nutrient-dependent growth rate of the phytoplankton species leads to higher catastrophes for the nutrient equilibrium manifold. The umbilic models are generalizations of the equations of organization of Eigen.
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    Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 761-775 
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    Notes: Abstract The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.
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    Some applications of the concept of body forces for the myocardium (1982)
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    Bulletin of mathematical biology 44 (1982), S. 819-840 
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    Notes: Abstract A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance.
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    On the stochastic theory of compartments: A semi-Markov approach for the analysis of theK-compartmental systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 809-817 
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    Notes: Abstract In this paper a semi-Markov process approach is developed to analyse stochastic compartmental systems using straightforward probabilistic arguments. Explicit expressions for several characteristics of thek-compartmental systems with a Poisson process input are derived and various models found in the literature arising from biological applications are generalised here using the semi-Markov process technique.
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    Analysis of a nonlinear diffusion problem With Michaelis-Menten kinetics by an integral equation method (1982)
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    Bulletin of mathematical biology 44 (1982), S. 841-849 
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    Notes: Abstract A mathematical model for oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is analyzed by means of an intergral equation method. It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem. Through an illustrative numerical calculation we are able to obtain an accurate solution for both the steady and transient problems. Finally, a comparison is made with the numerical solution of McElwain and the variational solution of Anderson and Arthurs for the steady state and Lin's result concerning the unsteady state.
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    A note on exact solutions of two prey-predator equations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 893-897 
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    Notes: Abstract Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species. The classes are defined by certain constraints which are imposed on the time-dependent parameters of the equations. A general result for such systems is that each species is characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.
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    Diffusion along intercellular spaces: An analysis of a transient situation (1982)
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    Bulletin of mathematical biology 44 (1982), S. 879-891 
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    Notes: Abstract We present an analysis of the diffusion of a tracer in a model of a cell-intercellular space system. The problem reduces to the resolution of a system of a linear partial differential equation and of a linear integral differential equation. The mathematical results have been obtained in terms of their Laplace transforms, which have been inverted by a numerical procedure for some parameter values. The importance of considering gradients of concentrations in intercellular spaces instead of lumping them with the external mediums has been discussed together with the possibility of extending Ussing's relation to transient cases, in order to detect active transports. Some possible implementations of the model to take into account more general situations have been considered.
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    Common source epidemics I: A stochastic model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 259-269 
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    Notes: Abstract A discrete time stochastic model is formulated for the spread of a disease which is transmitted to an uninfected but susceptible individual through an environmental source and not through contact (either direct or indirect) with infected individuals. The model incorporates both exposure and infection components. The exposure component includes consideration of the introduction of an infectious agent into the environment and the subsequent diffusion of the agent. It also includes time and location patterns for visits by individuals in the target population to the affected environment. The infection component incorporates physiological responses of exposed individuals to the infectious agent. The goal of the model is to provide a method for developing a predicted epidemic curve. Comments are given on an application of the model to the study of an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977.
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    Reply to letter by Jane Cronin (1982) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 450-450 
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    A kinetics model of abrin binding in a virus transformed lymphocyte cell culture (1982)
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    Bulletin of mathematical biology 44 (1982), S. 453-476 
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    Notes: Abstract The second order nonlinear differential equation $$\ddot x + \left( {\alpha _0 x + \alpha _1 } \right)\dot x + \alpha _2 x + \left( {x + \alpha _3 } \right) = 0$$ arises from a kinetics model of abrin binding in an Epstein-Barr virus-transformed lymphocyte culture. Some results on the dynamical behavior of this equation are given. These results are then discussed in relation to the known kinetics behavior of abrin in an EBV-lymphocyte cell culture.
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    Determination of dependence of binding parameters on receptor occupancy (1982)
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    Bulletin of mathematical biology 44 (1982), S. 477-489 
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    Notes: Abstract Measurements of the binding of ligand to receptors that are macromolecules, either free or components of biomembranes, often show deviation from what is expected of a simple reaction described by an association and a dissociation rate constant. A more versatile model and more discriminating experiments are required for a satisfactory explanation. This paper is based on a general model of the binding reaction in which the rate constants and equilibrium constant are dependent upon occupancy of receptors. The analysis of the model leads to three kinds of experiments: (1) equilibrium measurements which permit quantitative determination of a dissociation equilibrium parameter as a function of receptor occupancy; (2) measurements prior to equilibrium which yield the same information; and (3) measurements prior to equilibrium which reveal quantitatively the dependence of both association and dissociation rate parameters separately, on occupancy.
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    Solitary waves and macromolecular systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 705-713 
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    Notes: Abstract Macromolecules and their aggregates (such as protein bundles in biomembranes) possess polar modes which, when excited, tend to deform the system and call into play elastic restoring forces. A model of such systems, characterised typically by electric polarisation modes stabilised on the one hand by quartic self-interactions and on the other through coupling to the elastic deformations, admits the possibility of localised excitations (solitary waves) propagating with subsonic velocities, possessing the features of relative stability and efficient transport characteristics (associated with the collective nature of the phenomena), and at the same time provides a mechanism of control and variability which could be of considerable interest in biology.
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    Specific roles of the different boolean mappings in random networks (1982)
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    Bulletin of mathematical biology 44 (1982), S. 715-730 
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    Notes: Abstract Random Boolean networks have striking properties of self-organization. In this paper we propose an algorithm based on the different roles of Boolean mappings and on the connection structure to analyze the organization of the network. For a few cases— transfer mappings, AND/OR, equivalence/XOR—rigorous results are obtained about the dynamics of homogeneous networks. Conclusions are then drawn concerning the non-homogeneous networks.
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    A variational calculus approach to the suspension flow problem using the minimal force hypothesis (1982)
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    Bulletin of mathematical biology 44 (1982), S. 153-174 
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    Notes: Abstract Analytic expressions for the velocity profile and distribution of neutrally buoyant particles in laminar flow were obtained as functions of the radial distance. A modified Einstein viscosity model and the hypothesis that the total force on all the particles flowing in the tube is a minimum were used. The methods of the variational calculus were used in the mathematical development. A velocity profile differing only slightly from the parabolic form of that for Hagan-Poiseuille flow was obtained. For particle distribution the equations developed predict a maximum concentration along the center-line for some flows and a maximum concentration in a ring some distance from the center line in other flows. Both of these concentration profiles have been observed experimentally. Quantitative predictions from the equations derived must await further experimental work to permit calculation of the parameters included in the equations.
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    Electromagnetic mediated pharmacokinetics in a three-layer diffusional system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 215-229 
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    Notes: Abstract The effect of an applied electromagnetic field on drug diffusion in a one dimensional, three-layer drug-receptor model has been analyzed and expressed in terms of a normalized turnover rate parameter. The analysis reveals that an imposed harmonic time-varying electromagnetic field may enhance or retard the drug turnover rate depending on the diffusional pattern, the equivalent Michaelis constant, the maximum drug turnover rate of the intrinsic drug-receptor system, as well as the power density and frequency of the applied electromagnetic field. It is estimated that the power density in the order of magnitude of 1μW/cm2 at 100 MHz frequency range may be required to induce significant rate effects.
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    Large signal, low frequency characteristics of the systemic arterial system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 193-213 
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    Notes: Abstract A 4-parameter model to represent the relationship between slowly changing arterial inflow and the resulting pressure change was proposed. In order to determine values for the parameters and test the model in a wide range of pressure and flow, two experimental procedures were used. Firstly, slow oscillations in aortic pressure (period, 4 sec) were produced by means of an external pump connected to the aorta, and secondly, cardiac arrest was induced for about 2–3 sec by stimulating the right vagus. It was shown mathematically that the pressure and pump displacement information obtained in these experiments could be related to the model parameters. Values for the model parameters were obtained in 6 anesthetized dogs using a least squares adjustment procedure. Using aX 2-test, it was concluded that the model represented the arterial system for each animal well.
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    An asymmetrical kinetic model for veratridine interactions with sodium channels in molluscan neurons (1982)
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    Bulletin of mathematical biology 44 (1982), S. 231-258 
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    Notes: Abstract Veratridine alkaloid induces bi-stability or saw-tooth-shaped long potential waves in molluscan neurons. Voltage clamp experiments reveal the production of a slow sodium current whose changes are described by an asymmetric kinetic diagram relating the states of the sodium channels. Methods of the qualitative theory of differential equations were used to determine the condition necessary for such a model to have either an oscillatory solution or a bi-stable behavior. The kinetic diagram was modified to account for the frequency dependence of the slow sodium current production upon repeated short depolarizations. The modified kinetic diagram suggests that open and inactivated sodium channels are turned into channels with slow kinetic parameters; the transition from open channels would be fast, irreversible and restricted to part of the open channels, whereas that from inactivated channels would be slow and fully reversible upon repolarization.
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    Dissipative structures associated to certain reaction-diffusion equations in mathematical ecology (1982)
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    Bulletin of mathematical biology 44 (1982), S. 339-348 
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    Notes: Abstract Sufficient conditions are determined for the existence of stable spatially heterogeneous solutions of the Lotka-Volterra many species equations extended to include spatial diffusion. Some properties of such solutions are obtained. A general definition is proposed for the concept of a dissipative structure associated with a given reaction-diffusion equation. Finally, an approximate solution is presented for two interacting species in one spatial dimension, although the question of stability for this example is left open.
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    Common source epidemics II: Toxoplasmosis in Atlanta (1982)
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    Bulletin of mathematical biology 44 (1982), S. 377-398 
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    Notes: Abstract A discrete time stochastic model formulated for the study of common source epidemics (Shonkwiler and Thompson, 1982) is implemented to study an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977. A computer simulation program is described and conclusions are drawn on the basis of the simulations. Also, the detailed empirical data are organized to illuminate the roles of visitation and location patterns, and the variation in the empirical epidemic curve with different reporting schemes.
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    Film models for multicomponent mass transfer: Diffusion in physiological gas mixtures (1982)
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    Bulletin of mathematical biology 44 (1982), S. 361-376 
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    Notes: Abstract The exact solution of the Maxwell-Stefan equations for steady state diffusion in a stagnant film due to Krishna and Standart (1976) is compared to the approximate solutions of Toor (1964) and Stewart and Prober (1964) for osmotic diffusion of oxygen in the three physiological gas mixtures He−N2−O2, He−SF6−O2, N2−SF6−O2. It is found that the predicted fluxes of He, N2 and SF6 are usually in excellent agreement but that the two methods could predict differing directions of transfer of oxygen. Concentration profiles obtained from the linearized equations may be significantly different from the profiles calculated from an exact solution of the film model.
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    A generalization of the optimal models of arterial branching (1982)
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    Bulletin of mathematical biology 44 (1982), S. 349-360 
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    Notes: Abstract Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr 3, as proposed by Murray in 1926. An exception is the model of Uylings (1977), in which he allowed the exponent ofr to vary from 2.33 to 3.0. Theoretical considerations coupled with empirical evidence suggest that the cubic flow equation may not be appropriate to describe the branching pattern of the arterial tree. The optimal models are modified to accommodate a more general flow equationf=kr x . Models that minimize a geometric feature such as surface or volume are sensitive to variations inx in a different way from those which minimize flow-related parameters, such as power loss due to friction and shear stress.
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    Distribution of survival times in the Fix and Neyman model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 587-591 
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    Notes: Abstract In this paper we consider a general illness-death stochastic model in which the transition intensities all vary proportionally to a time function ϕ(t). We extend Chiang's earlier work to include processes which are both reversible and have parameters which are time varying, and obtain survival time distributions and the expectation and variance of survival times.
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    Local geometry of arterial branching (1982)
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    Bulletin of mathematical biology 44 (1982), S. 597-607 
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    Notes: Abstract A model of the geometrical structure of arterial bifurcations is proposed in the context of optimality of the bifurcation as a fluid conducting system. Optimality is considered both globally, in terms of the cardiovascular system as a whole, and locally, in terms of the orderliness of the flow in the bifurcation region. It is shown that a bifurcation can be optimal both globally and locally. Typical examples of such bifurcations are given.
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    Simulation of chemical oscillations in membranes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 637-645 
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    Notes: Abstract A computer simulation model has been developed to follow chemical oscillations in a membrane for immobilized enzyme systems. It is a discrete particle type model which follows the spatial and temporal fluctuations of the concentrations in a reaction involving two substrates. The parameters can be readily varied to allow dissipative structures to result from the sustained nonlinear reaction kinetics and to determine which parameters cause damping of the oscillations. The nature of the diffusion mechanism allows extension to more than one dimension.
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