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
Self-tolerance and autoimmunity in a regulatory T cell model.
Helen K. Alexander,Lindi M. Wahl +1 more
TL;DR: Irrespective of mechanism, the model predicts that Tregs specific for the autoantigen in question play no role in the system’s qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels.
Journal ArticleDOI
Interspecific influence on mobility and Turing instability.
Yunxin Huang,Odo Diekmann +1 more
TL;DR: A multi-patch multi-species model in which the percapita emigration rate of one species depends on the density of some other species focuses on Turing instability to examine if and when this cross-emigration response has crucial effects.
Stability analysis of a discrete ecological model
Qamar Din,E. M. Elsayed +1 more
TL;DR: In this article, the qualitative behavior of following discrete-time population model was studied and the existence and uniqueness of positive equilibrium point, boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium points of this model was investigated.
Journal ArticleDOI
A structural classification of candidate oscillatory and multistationary biochemical systems.
TL;DR: A classification for sign-definite non-autocatalytic biochemical networks is proposed, which summarizes several existing results in the literature and calls weak ( strong) candidate oscillators systems those which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while weak (strong) candidate multistationary systems are called.
Journal ArticleDOI
A diffusion model for dispersal of Opuntia imbricata (cholla) on rangeland
TL;DR: A theoretical model is formulated for the dispersal of plants based on the diffusion equation which assumes one or more mechanisms of dispersal (e.g. passive and active dispersal) are assumed.