Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession* *M Wang was supported by NSFC Grant 11771110, Q Zhang was supported by the China Scholarship Council, and X-Q Zhao was supported by the NSERC of Canada.

Abstract

In this paper, we investigate the propagation dynamics of a reaction–diffusion competition model with seasonal succession in the whole space. Under the weak competition condition, the corresponding kinetic system admits a globally stable positive periodic solution . By the method of upper and lower solutions and the Schauder fixed point theorem, we first obtain the existence and nonexistence of traveling wave solutions connecting (0, 0) to . Then we use the comparison arguments to establish the spreading properties for a large class of solutions.