Sponsor
This work was partially supported by the NSF under grants DMS-0818050, DMS-1014817 and DMS- 1211635.
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.
DOI
10.1080/17513758.2012.714478
Persistent Identifier
http://archives.pdx.edu/ds/psu/10604
Citation Details
De Leenheer, Patrick; Gopalakrishnan, Jay; and Zuhr, Erica, "Instability in a Generalized Keller–Segel model" (2012). Mathematics and Statistics Faculty Publications and Presentations. 36.
http://archives.pdx.edu/ds/psu/10604
Description
This is an Author's Accepted Manuscript of an article published in Journal of Biological Dynamics, Vol. 6 Issue 2, March 2012. Copyright Taylor & Francis, available online at: http://www.tandfonline.com/