Pattern formation in a generalized Keller-Segel model

Details Pattern formation in a generalized Keller-Segel model Pattern formation in a generalized Keller-Segel model

2011-10-11

arxiv.org/abs/1110.2448v1

Mathematics

Analysis of PDEs

Scientific paper

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. This points to new avenues to explain pattern formation, distinct from the traditional Turing instability.

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