Instability in a generalized multi-species Keller-Segel chemotaxis model

In this paper we discuss Turing instability of a generalized Keller-Segel chemotaxis model involving n-species and m-chemoattractants. By using combinatorial matrix theory we extend the result on the instability of a single-species and n-chemicals Keller-Segel system (Leenheer et al., 2012) to a general (n+m)×(n+m) system. A sufficient condition for chemotaxis driven Turing instability of the multi-species model is obtained. Moreover, some examples and numerical simulations are presented to illustrate the theoretical results.