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
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Journal Article
Multiple time scales in consumer-resource interactions
TL;DR: This work defines three natural time scales for consumer-resource interactions and demonstrates, using asymptotic methods of analysis, how relative differences in these scales lead to the formulation of models with qualitatively distinct dynamics.
Journal ArticleDOI
Towards an integrated systems-based modelling framework for drug transport and its effect on tumour cells
TL;DR: The modelling framework developed in this study provides qualitative and mechanistic insights into the effect of drug on tumour cells and provides an in silico experimental platform to investigate the interplay between extracellular factors and intracellular factors.
Journal ArticleDOI
Hydra effects in discrete-time models of stable communities
TL;DR: Hydro effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models are shown.
Journal ArticleDOI
Resilience in a two-population system: interactions between Allee effects and connectivity
Carter L. Johnson,Alan Hastings +1 more
TL;DR: The result is a mathematical model that justifies the assumption that resilience can be averaged across connected populations and suggests several management strategies to either avoid or induce regime shift cascades.
Journal ArticleDOI
An alternative approach to Michaelis-Menten kinetics that is based on the Renormalization Group.
TL;DR: In this paper, an alternative approach to the study of Singularly Perturbed Differential Equations, based on the Renormalization Group (SPDERG), is presented.