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
Robust Control Design for Linear Systems Using an Ecological Sign-Stability Approach
TL;DR: The concept of qualitative stability was introduced in the field of population biology and ecology by as mentioned in this paper, where the authors considered a large-scale system in which there is no quantitative information about the interrelationship of species or subsystems.
Journal ArticleDOI
A nonlinear two-species oscillatory system: bifurcation and stability analysis
TL;DR: In this article, the authors deal with nonlinear bifurcation analysis of two-species oscillatory system consisting of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system.
Journal ArticleDOI
Mathematical and computational modeling in biology at multiple scales
Jack A. Tuszynski,Philip Winter,Diana White,Chih-Yuan Tseng,Kamlesh Kumar Sahu,Francesco Gentile,Ivana Spasevska,Sara Ibrahim Omar,Niloofar Nayebi,Cassandra D. M. Churchill,Mariusz Klobukowski,Rabab M. Abou El-Magd +11 more
TL;DR: A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms.
Journal ArticleDOI
The possible role of reaction-diffusion in leaf shape.
TL;DR: These models show that diverse leaf shapes may be obtained from a single reaction–diffusion system, and have implications in terms of both convergent and divergent evolution.
Journal ArticleDOI
Reaction diffusion modelling of biological pattern formation: Application to the embryogenesis of Drosophila melanogaster
TL;DR: In this article, a specific biological problem, the origin of the segmentation pattern in the fruit fly Drosophila melanogaster, is discussed, and the general plan of computational work to study how this could arise by reaction-diffusion is indicated.