Spreading Speeds for Two Species Competition Systems in Time Almost Periodic and Space Periodic Media

Abstract

The current paper is devoted to the study of the spreading speeds of two species competition diffusion-advection systems in time almost periodic and space periodic media. We first show that there is a finite spreading speed interval for such diffusion-advection systems. The principal Lyapunov exponent and the principal Floquent bundle theory have been applied to study the spreading speed of time almost periodic and space periodic systems. Under some sufficient conditions, we prove that the spreading speed interval of such systems in any direction is a singleton in the partially spatially homogeneous case and the general case, respectively.