Title
Mathematical aspects of pattern formation in biological systems [electronic resource] / Juncheng Wei, Matthias Winter.
ISBN
9781447155263 electronic book
1447155262 electronic book
9781447155256
Published
London : Springer, [2013?]
Copyright
©2014
Language
English
Description
1 online resource (xii, 319 pages) : illustrations.
Item Number
10.1007/978-1-4471-5526-3 doi
Call Number
QH323.5
Dewey Decimal Classification
570.1/5118
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from PDF title page (SpringerLink, viewed September 24, 2013).
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v.189.
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.
