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  • 1
    Electronic Resource
    Electronic Resource
    Frequency Modulation Dynamics in Neural Networks (1987)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 504 (1987), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1987.tb48725.x
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  • 2
    Electronic Resource
    Electronic Resource
    NONUNIQUE STABLE RESPONSES OF EXTERNALLY FORCED OSCILLATORY SYSTEMS (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 316 (1979), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1979.tb29493.x
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis of a stable polymorphism arising in a selection-migration model in population genetics (1975)
    Springer
    Journal of mathematical biology 2 (1975), S. 235-240 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary This investigation studies the dynamic behaviour of a population in which there is a geographic variation in fitness of a one-locus, two allele trait. The results derived here complement certain results by W. H. Fleming who described the existence of a stable polymorphism when the ratio of selection intensity to dispersion rate exceeds a critical value. Here an approximation to the polymorphic state is obtained, and the evolution of other initial states to it is studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277152
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  • 4
    Electronic Resource
    Electronic Resource
    Phase locking of biological clocks (1982)
    Springer
    Journal of mathematical biology 15 (1982), S. 339-349 
    Details
    ISSN: 1432-1416
    Keywords: Biological clocks ; Nonlinear oscillations ; Phase locking ; Method of averaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Radial isochron clocks (RICs) and their response to external signals and coupling with other RICs are studied. RICs are derived as phase approximations to self-sustained oscillators. Their response to single impulses (phase resetting) and to repetitive impulses is determined. This response may be harmonic or chaotic. Finally, the effect of coupling between clocks is studied. Simple coupling is shown to exhibit rhythm splitting like that observed in fish and small mammals. New phase locking results for general weakly coupled RIC systems are also derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275692
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  • 5
    Electronic Resource
    Electronic Resource
    A mathematical analysis of small mammal populations (1987)
    Springer
    Journal of mathematical biology 25 (1987), S. 263-274 
    Details
    ISSN: 1432-1416
    Keywords: Population biology ; Nonlinear renewal theory ; Population waves: synchronization ; Rarefaction and compression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Populations of Microtus montanus, the montane vole, have been extensively studied. It is known that their reproductive activity is closely linked to the availability of the chemicals in growing plants. We use a mathematical model here to study how the length of the vegetative season and the natural reproduction rhythm of voles are involved in the long term dynamics of the population numbers. In particular, we use data obtained from Timpie Springs, Utah, and from Jackson Hole, Wyoming, to formulate a model. The novelty of this model is its use of littering curves that highlight the temporally discrete nature of vole reproduction. The model shows how the timing of the vegetative season can influence vole population sizes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276436
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  • 6
    Electronic Resource
    Electronic Resource
    Wave propagation in mathematical models of striated cortex (1997)
    Springer
    Journal of mathematical biology 35 (1997), S. 988-994 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050086
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  • 7
    Electronic Resource
    Electronic Resource
    The searchlight hypothesis (1991)
    Springer
    Journal of mathematical biology 29 (1991), S. 689-691 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00163919
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  • 8
    Electronic Resource
    Electronic Resource
    Book reviews (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 287-291 
    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/BF02458448
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  • 9
    Electronic Resource
    Electronic Resource
    Discrete time semigroup transformations with random perturbations (1997)
    Springer
    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    Details
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02227491
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  • 10
    Electronic Resource
    Electronic Resource
    Conditions for sympatric speciation: A diploid model incorporating habitat fidelity and non-habitat assortative mating (1996)
    Springer
    Evolutionary ecology 10 (1996), S. 187-205 
    Details
    ISSN: 1573-8477
    Keywords: speciation ; habitat-sympatric divergence ; divergent selection ; habitat preference ; assortative mating ; linkage disequilibrium ; penetrance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Three types of genes have been proposed to promote sympatric speciation: habitat preference genes, assortative mating genes and habitat-based fitness genes. Previous computer models have analysed these genes separately or in pairs. In this paper we describe a multilocus model in which genes of all three types are considered simultaneously. Our computer simulations show that speciation occurs in complete sympatry under a broad range of conditions. The process includes an initial diversification phase during which a slight amount of divergence occurs, a quasi-equilibrium phase of stasis during which little or no detectable divergence occurs and a completion phase during which divergence is dramatic and gene flow between diverging habitat morphs is rapidly eliminated. Habitat preference genes and habitat-specific fitness genes become associated when assortative mating occurs due to habitat preference, but interbreeding between individuals adapted to different habitats occurs unless habitat preference is almost error free. However, ‘nonhabitat assortative mating’, when coupled with habitat preference can eliminate this interbreeding. Even when several loci contribute to the probability of expression of non-habitat assortative mating and the contributions of individual loci are small, gene flow between diverging portions of the population can terminate within less than 1000 generations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01241784
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