A time-periodic diffusive prey–predator model with sign-changing growth rates and a free boundary

Abstract

We undertake a study of a free boundary problem for a diffusive prey–predator model in the heterogeneous time-periodic environment, in which the local growth rates of two species may change signs and be very “negative” in a “suitable large region” (see the conditions (H1) and (H2)). We investigate the spreading–vanishing dichotomy, long-time dynamical behavior of the solution, criteria for spreading and vanishing, and estimates of the asymptotic spreading speed of the free boundary. As an off-shoot of our analysis, we also obtain the existence of positive solutions to a T-periodic boundary value problem on half line associated with our free boundary problem.