The time-periodic diffusive competition models with a free boundary and sign-changing growth rates

Abstract

To understand the spreading of invasive and native species, in this paper we consider the diffusive competition models with a free boundary in the heterogeneous time-periodic environments, in which the variable intrinsic growth rates of these two species change signs and may be very negative in some large regions. We study the spreading–vanishing dichotomy, long-time dynamical behavior of solution, sharp criteria for spreading and vanishing, and estimates of the asymptotic spreading speed of the free boundary. Moreover, we establish the existence of positive solutions to a T-periodic boundary value problem of the diffusive competition system with sign-changing growth rates in the half line.