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Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth

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  • Haiyan Gao
  • Shengmao Fu

Abstract

This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a -dimensional box . It is proved that given any general perturbation of magnitude , its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order . Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns.

Suggested Citation

  • Haiyan Gao & Shengmao Fu, 2014. "Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, July.
    • Handle: RePEc:hin:jnlaaa:248657
    DOI: 10.1155/2014/248657
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