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Instability in a Generalized Keller–Segel model
Journal of Biological Dynamics
  • Patrick De Leenheer, University of Florida
  • Jay Gopalakrishnan, Portland State University
  • Erica Zuhr, High Point University
Document Type
Publication Date
  • Pattern formation (Biology),
  • Morphogenesis,
  • Arbitrary constants,
  • Chemotaxis
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.

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:

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Citation Information
Patrick De Leenheer, Jay Gopalakrishnan and Erica Zuhr. "Instability in a Generalized Keller–Segel model" Journal of Biological Dynamics (2012)
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