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 ArticleDOI
Modeling cellular processes in 3D
Alex Mogilner,David J. Odde +1 more
TL;DR: Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.
Journal ArticleDOI
On the system of two difference equations of exponential form: xn+1=a+bxn−1e−yn,yn+1=c+dyn−1e−xn
TL;DR: It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form.
Journal ArticleDOI
Dynamics of a plant–herbivore model
TL;DR: A simple host–parasite type model to study the interaction of certain plants and herbivores and suggests two control strategies: reducing the population of the herbivore under some threshold or increasing the growth rate of the plant leaves.
Journal ArticleDOI
Linear discrete models with different time scales
TL;DR: In this article, the authors extend aggregation methods to time-discrete models of population dynamics and compare the asymptotic behaviors of both systems which are shown to be similar to a certain order.
Journal ArticleDOI
Characterizing the dynamics of the quorum-sensing system in Staphylococcus aureus.
TL;DR: The virulence determinants of Staphylococcus aureus are expressed in a growth phase-dependent manner governed by the autoinducible quorum-sensing system agr, and the effect of adding inhibitors to the system was analyzed to better understand how SarA would affect activation of the agr system by modulating the basal agr activity.