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  • Articles  (44,609)
  • Springer  (44,609)
  • 2020-2024
  • 1980-1984  (44,609)
  • 1982  (44,609)
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  • 2020-2024
  • 1980-1984  (44,609)
Year
Journal
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  • 1
    Electronic Resource
    Electronic Resource
    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459415
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  • 2
    Electronic Resource
    Electronic Resource
    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459417
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  • 3
    Electronic Resource
    Electronic Resource
    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459418
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459420
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  • 5
    Electronic Resource
    Electronic Resource
    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459419
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  • 6
    Electronic Resource
    Electronic Resource
    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459421
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  • 7
    Electronic Resource
    Electronic Resource
    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
    Details
    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).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459422
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  • 8
    Electronic Resource
    Electronic Resource
    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 149-150 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459425
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  • 9
    Electronic Resource
    Electronic Resource
    Transient effects on the initial rate of oxygenation of red blood cells (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 119-134 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459423
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  • 10
    Electronic Resource
    Electronic Resource
    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 537-547 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459407
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