Nonlinear Instability For A Two Species And Two Chemotactic Factors Keller-Segel Model

In this paper, we consider the nonlinear instability of the positive equilibrium point for a two species and two chemotactic factors Keller-Segel model in domain T~d= (0,?)~d(d?3). Growing modes of nonlinear evolution to the model (1) is discussed by applying the Sobolev embedding theorem, the energy estimates and the bootstrap arguments. It is proved that the positive equilibrium point of linear instability is nonlinearly unstable for the model and its small perturbation can lead to spatial and temporal patterns.