Mathematical Aspects of Pattern Formation in Biological Systems (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
319
Utgivningsdatum
2016-08-27
Upplaga
Softcover reprint of the original 1st ed. 2014
Förlag
Springer London Ltd
Medarbetare
Winter, Matthias
Illustrationer
20 Illustrations, black and white; XII, 319 p. 20 illus.
Dimensioner
234 x 156 x 18 mm
Vikt
468 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9781447172611
Mathematical Aspects of Pattern Formation in Biological Systems (häftad)

Mathematical Aspects of Pattern Formation in Biological Systems

av Juncheng Wei, Matthias Winter
Häftad,  Engelska, 2016-08-27
1314
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This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: * Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones * Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions * Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.
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From the book reviews: "This book deals with the mathematical analysis of patterns encountered in biological systems, using a variety of functional analysis methods to prove the existence of solutions. ... It is indeed written for advanced graduates and experts interested in the mathematics of pattern formation and reaction-diffusion equations. ... this is a good reference source for various advanced theories and mathematical applications in this field." (J. Michel Tchuenche, zbMATH, Vol. 1295, 2014)

Innehållsförteckning

Introduction.- Existence of spikes for the Gierer-Meinhardt system in one dimension.- The Nonlocal Eigenvalue Problem (NLEP).- Stability of spikes for the Gierer-Meinhardt system in one dimension.- Existence of spikes for the shadow Gierer-Meinhardt system.- Existence and stability of spikes for the Gierer-Meinhardt system in two dimensions.- The Gierer-Meinhardt system with inhomogeneous coefficients.- Other aspects of the Gierer-Meinhardt system.- The Gierer-Meinhardt system with saturation.- Spikes for other two-component reaction-diffusion systems.- Reaction-diffusion systems with many components.- Biological applications.- Appendix.

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