Mathematical Aspects of Pattern Formation in Biological Systems

• Main Authors: Wei, Juncheng (Author), Winter, Matthias (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2014.
• Series: Applied Mathematical Sciences, 189
• Subjects: Mathematics.; Partial differential equations.; Biomathematics.; Partial Differential Equations.; Mathematical and Computational Biology.; Genetics and Population Dynamics.; Physiological, Cellular and Medical Topics.

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 p...

Table of Contents:

• 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.