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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On synchronous behavior in complex nonlinear dynamical systems
TL;DR: The focus of the first main part of this dissertation is on the application of contraction theory and graph theory to synchronization in complex interacting systems that can be modeled as an interconnected network of identical systems.
The evolution of bacterial cell differentiation and multicellular organization
TL;DR: In this paper, a combinatie van experimenten and theorie is presented to show how simplistisch the kijk op bacterien is, and how cellen evolueren over time.
Journal ArticleDOI
Uniqueness and global attractivity of glycolytic oscillations suggested by Selkov's model
TL;DR: In this article, the qualitative properties of the model proposed by Selkov Eur J Biochem 4: 79-86 (1968) for the description of the glycolytic oscillations are studied.
Journal ArticleDOI
Does quasi-local competition lead to pattern formation in metapopulations? An explicit resource competition model
TL;DR: This work derives a model for quasi-local competition from first principles, assuming that individuals compete for shared resources and members of a population spend a certain fraction of their foraging time in the adjacent populations.
Journal ArticleDOI
Modelling contact spread of infection in host–parasitoid systems: Vertical transmission of pathogens can cause chaos
Katharine F. Preedy,Pieta Schofield,Sijia Liu,Anastasios Matzavinos,Mark A. J. Chaplain,Stephen F. Hubbard +5 more
TL;DR: A mathematical model of contact spread infection is developed to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model and shows that the transient and long-term dynamics exhibited under contact spread infections are highly complex.