Asymptotic behavior and multiplicity for a diffusive Leslie–Gower predator–prey system with Crowley–Martin functional response

A diffusive predator–prey system with modified Leslie–Gower and Crowley–Martin functional response is considered. The extinction and permanence of the time-dependent system are determined by virtue of the comparison principle. Then, the sufficient and necessary conditions for the existence of coexistence states are obtained. Furthermore, the stability, uniqueness and exact multiplicity of coexistence states are investigated by means of the combination of the perturbation theory, bifurcation theory and degree theory. Our results indicate that c1c1 have an effect on the stability and exact multiplicity of coexistence states. Finally, some numerical simulations are presented to verify and complement the theoretical results.