Published In

Journal of Biological Dynamics

Document Type

Post-Print

Publication Date

2012

Subjects

Pattern formation (Biology), Morphogenesis, Arbitrary constants, Chemotaxis

Abstract

We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although this mechanism was already known to exist in the original Keller–Segel model, here we show that it is more generally applicable by significantly enlarging the class of models exhibiting this instability phenomenon which may lead to pattern formation.

Rights

Copyright 2012 Taylor & Francis

Description

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Biological Dynamics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Biological Dynamics, Vol. 6 Issue 2, March 2012.

DOI

10.1080/17513758.2012.714478

Persistent Identifier

http://archives.pdx.edu/ds/psu/10604

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Mathematics Commons

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