Periodic Bistable Traveling Waves for a Non-Local Dispersal Competition System with Seasonal Succession

In this paper, we are devoted to the study of periodic bistable traveling waves of a non-local dispersal competition system with seasonal succession in the whole space. This system can be used to describe the propagation of two competitive species in bad and good seasons. By a special change of variables, we transform this competitive system into a cooperative system. Then, we pay attention to the existence and stability of periodic bistable traveling waves for this special cooperative system. By applying the abstract monotone semiflow approach, we first obtain the existence of periodic bistable traveling waves. Then, by constructing suitable upper-lower solutions and using a dynamical system approach, we prove the global stability of periodic bistable traveling waves.