Bistable pulsating wave of a competition model in rapidly varying media and its homogenization limit

Abstract

This paper is concerned with the existence of bistable pulsating wave for a two-species competition system in rapidly periodically varying media and its homogenization limit as the spatial period tends to zero. Assuming that the homogenized system admits a bistable traveling wave, we first show the existence of pulsating wave for all small periods and determine the homogenization limit of the wave speed. Furthermore, in the case where the homogeneous wave is not stationary, we investigate the effects of spatial heterogeneity on the wave speeds. Our estimates indicate that the deviation of the wave speeds in comparison to the homogeneous one is at most linearly along with small period in the general case, and is of second order where the heterogeneity appears only in the diffusion coefficients.