Bistable travelling waves for a reaction and diffusion model with seasonal succession**Research supported in part by the NSERC of Canada and the MITACS of Canada.

Abstract

This paper is devoted to the study of a periodic reaction–diffusion competition model, which describes the propagation of two competitive species in bad and good seasons. The existence and global stability of time-periodic bistable travelling waves are established for such a system under appropriate conditions. The methods involve the upper and lower solutions, spreading speeds of monostable systems, and the monotone semiflows approach.