文章基本信息

标题：Instability in a generalized Keller–Segel model
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作者：Patrick De Leenheer ; Jay Gopalakrishnan ; Erica Zuhr 等
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2012
卷号：6
期号：2
页码：974-991
DOI：10.1080/17513758.2012.714478
出版社：Taylor & Francis
摘要：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.
关键词：chemotaxis; Keller–Segel; steady state; stability; pattern formation; Turing instability