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
Developmental Models and Polygenic Characters
TL;DR: The consequences of a simple nonlinear model of development based on the mechanism believed to be responsible for the determination of eyespot patterns on the wings of butterflies are explored.
Journal ArticleDOI
Translational Systems Approaches to the Biology of Inflammation and Healing
Yoram Vodovotz,Gregory M. Constantine,James R. Faeder,Qi Mi,Jonathan E. Rubin,John Bartels,Joydeep Sarkar,Robert H. Squires,David O. Okonkwo,Jörg C. Gerlach,Ruben Zamora,Shirley Luckhart,G. Bard Ermentrout,Gary An +13 more
TL;DR: An iterative and ongoing program of literature analysis, generation of prospective data, data analysis, and computational modeling in various experimental and clinical inflammatory disease settings has suggested how to modulate acute inflammation in a rational, individually optimized fashion.
Journal ArticleDOI
Models for the length distributions of actin filaments: I. Simple polymerization and fragmentation.
TL;DR: This paper investigates what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
Journal ArticleDOI
Transient behavior of biological loop models with application to the droop model
Olivier Bernard,Jean-Luc Gouzé +1 more
TL;DR: The transient behavior of a class of nonlinear differential systems verifying sign conditions through the succession of extrema of the state variables is studied and the global stability of the equilibrium and the possible successions of the extremas are obtained.
Journal ArticleDOI
The effect of dispersal on population growth with stage-structure☆
TL;DR: In this article, a conservation strategy is proposed by introducing and analyzing the asymptotic behavior of some autonomous and time-varying population models, and the biological implications of these results are discussed briefly.