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.
Haiyan Gao. Shengmao Fu. "Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth." Abstr. Appl. Anal. 2014 (SI66) 1 - 11, 2014. https://doi.org/10.1155/2014/248657