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

Abstract EN

This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d -dimensional box T d = ( 0 , π ) d ( d = 1,2 , 3 ) .

It is proved that given any general perturbation of magnitude δ , 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 ln ( 1 / δ ) .

Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns.