Mathematical Aspects of Pattern Formation in Biological Systems - Juncheng Wei, Matthias Winter

Mathematical Aspects of Pattern Formation in Biological Systems

Buch | Softcover
319 Seiten
2016 | Softcover reprint of the original 1st ed. 2014
Springer London Ltd (Verlag)
978-1-4471-7261-1 (ISBN)
90,94 inkl. MwSt
Focusing on large-amplitude patterns far from equilibrium in biologically relevant models, this book summarizes and expands on fifteen years of results in the mathematical analysis of patterns which are encountered in biological systems.
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.

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.

Erscheinungsdatum
Reihe/Serie Applied Mathematical Sciences ; 189
Zusatzinfo 20 Illustrations, black and white; XII, 319 p. 20 illus.
Verlagsort England
Sprache englisch
Maße 155 x 235 mm
Themenwelt Informatik Weitere Themen Bioinformatik
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Biologie Evolution
Schlagworte Biological Systems • Computational Biology • Genetics Dynamics • Localised Structures • Mathematical Analysis • Mathematical Biology • Partial differential equations • pattern formation • population dynamics • reaction-diffusion systems • singular perturbation • stability
ISBN-10 1-4471-7261-2 / 1447172612
ISBN-13 978-1-4471-7261-1 / 9781447172611
Zustand Neuware
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