TURING PATTERNS OF A PREDATOR–PREY MODEL WITH A MODIFIED LESLIE–GOWER TERM AND CROSS-DIFFUSIONS

Abstract

In this paper, a strongly coupled diffusive predator–prey system with a modified Leslie–Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns.