Effects of temporal variations on wave speeds of bistable traveling waves for Lotka-Volterra competition systems

Abstract: This paper investigates the bistable traveling waves for two-species Lotka-Volterra competition systems in time periodic environments. We focus especially on the influence of the temporal period, with existence results established for both small and large periods.We also show the existence of, and derive explicit formulas for, the limiting speeds as the period tends to zero or infinity, and provide estimates for the corresponding rates of convergence. Furthermore, we analyze the sign of wave speed. Assuming that both species share identical diffusion rates and intraspecific competition rates, we obtain a criterion for determining the sign of wave speed by comparing the intrinsic growth rates and interspecific competition strengths. More intriguingly, based on our explicit formulas for the limiting speeds, we construct an example in which the sign of wave speed changes with the temporal period. This example reveals that temporal variations can significantly influence competition outcomes,enabling different species to become dominant under different periods.