MonographDOI
Mathematical Models in Biology
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TLDR
The theory of linear difference equations applied to population growth and the applications of nonlinear difference equations to population biology are explained.Abstract:
Part I. Discrete Process in Biology: 1. The theory of linear difference equations applied to population growth 2. Nonlinear difference equations 3. Applications of nonlinear difference equations to population biology Part II. Continuous Processes and Ordinary Differential Equations: 4. An introduction to continuous models 5. Phase-plane methods and qualitative solutions 6. Applications of continuous models to population dynamics 7. Models for molecular events 8. Limit cycles, oscillations, and excitable systems Part III. Spatially Distributed Systems and Partial Differential Equation Models: 9. An introduction to partial differential equations and diffusion in biological settings 10. Partial differential equation models in biology 11. Models for development and pattern formation in biological systems Selected answers Author index Subject index.read more
Citations
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Journal ArticleDOI
Chemical Oscillations in Enzyme Kinetics
TL;DR: This work has compared the Higgins model with the other two variable models and found that the origin of the richer dynamical behavior of the Higginsmodel is due to the enzymatic step in the mechanism.
Journal ArticleDOI
Risk assessment of the harvested pike-perch population of the Azov Sea
TL;DR: In this paper, a stochastic simulation model is developed to assess simultaneously the annual yield and the extinction risk of the exploited population resulting from different harvesting strategies (i.e. combinations of harvesting efforts on yearlings and on adults).
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Pattern formation (II): The Turing Instability
Yan Guo,Hyung Ju Hwang +1 more
TL;DR: In this paper, the authors consider the classical Turing instability in a reaction-diffusion system and prove that the nonlinear dynamics of a general perturbation of the Turing instability is determined by the finite number of linear growing modes over a time scale of
Journal ArticleDOI
A kinetic model for Brain-Derived Neurotrophic Factor mediated spike timing-dependent LTP
TL;DR: The role of BDNF/TrkB signaling in spike-timing dependent plasticity (STDP) in rodent hippocampus CA1 pyramidal cells is investigated by implementing the first subcellular model ofBDNF regulated, spike timing-dependent long-term potentiation (t-LTP), which points out a few predictions on how to enhance LTP induction in such a way to rescue or improve cognitive functions under pathological conditions.
Multi-scaling methods applied to population models
TL;DR: This dissertation presents several applications of the multi-scaling (multi-timing) technique to the analysis of both single and two species population models where the defining parameters vary slowly with time.