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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Stability in a discrete prey-predator model
Sagaya Raj,Maria Selvam +1 more
TL;DR: In this paper, the discrete-time predator-prey model in 2-dimensions is investigated and phase portraits are obtained for different sets of parameter values and initial conditions and bifurcation diagrams are presented for selected range of growth parameter.
Book ChapterDOI
Monotone and near-monotone systems
TL;DR: In this article, an expository introduction to monotone and near-monotone biochemical network structures is provided, which suggests that natural biological systems may have evolved to be at least close to monotonous.
Journal ArticleDOI
The population dynamics of black-white-mulatto racial systems.
TL;DR: It is shown that “bounded” patterns of racial classification and switching imply long-run racial homogeneity in the absence of differential reproduction, which accounts for the dramatic growth of the white population share in Puerto Rico in the early 20th century.
Posted ContentDOI
Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics
TL;DR: By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, this work presents the first modelling framework that gives rise to a range of global Allee effects.
Journal ArticleDOI
Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group
TL;DR: A pedagogical study of some aspects of the size of this limit cycle using perturbative renormalization group by doing detailed and explicit calculations upto second order for the Selkov model for glycolytic oscillations.