Spreading speed of a lattice time-periodic Lotka–Volterra competition system with bistable nonlinearity

Abstract

We study the uniqueness and sign of bistable wave speed for a lattice time-periodic Lotka–Volterra competition system of bistable type. The sign of wave speed reflects the propagation direction of traveling wave which arises as a challenging problem in the field of traveling wave theory. Actually, even for the case of homogeneous environment, there is no common method that can be used to deal with it. First, we show that the speed of the bistable wave of the model is unique. Second, by making use of upper–lower solution method and comparison principle, a set of explicit conditions is built up such that the sign of the wave speed can be justified. From the viewpoint of biology, these conditions reveal which of the species will tend to extinction and which will survive when the environment changes periodically in time.