Speed selection of wavefronts for lattice Lotka-Volterra competition system in a time periodic habitat

Abstract

In this paper, the speed selection for the time periodic traveling wave solutions of a two-species competition lattice model of diffusive Lotka-Volterra type is investigated. By using the upper-lower solution method, an abstract result and several explicit sufficient conditions for linear selection are established. Moreover, a general condition for nonlinear selection is also obtained, which indicates that the minimal speed is nonlinearly selected if the system admits a lower solution with faster decay at the far end. Based on this result, some explicit conditions for nonlinear selection are found by constructing novel lower solutions.