Dublin Core
Title
Mathematics and Life Sciences : Chapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology
Subject
Numerical analysis
Applied mathematics
Description
In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology.
Creator
Marciniak-Czochra, Anna
Source
http://library.oapen.org/handle/20.500.12657/23720
Publisher
De Gruyter
Date
2012
Contributor
Ani
Rights
https://creativecommons.org/licenses/by/4.0
Format
Pdf
Language
English
Type
Books
Identifier
DOI 10.1515/9783110288537.191
ISBN 9783110273724