Periodic solutions of a non-autonomous predator–prey system with migrating prey and disease infection: via Mawhin’s coincidence degree theory

Abstract

In this paper, we consider a non-autonomous competitive predator–prey system with migrating prey and disease infection in both species. Based on some novel estimation techniques for the prior bound and Mawhin’s coincidence degree theorem, some sufficient conditions for the permanence and existence of periodic solutions are obtained. A suitable Lyapunov function was constructed to prove the global asymptotical stability of the positive periodic solution. Finally, an example and its numerical simulations demonstrate the validity of the results.