Propagation dynamics for a class of integro-difference equations in a shifting environment

Abstract

In this paper, we study the propagation dynamics for a class of integro-difference equations with a shifting habitat. We first use the moving coordinates to transform such an equation to an integro-difference equation with a new kernel function containing the shifting speed c. In two directions of the spatial variable, the resulting equation has two limiting equations with spatial translation invariance. Under the hypothesis that each of these two limiting equations has both leftward and rightward spreading speeds, we establish the spreading properties of solutions and the existence of nontrivial forced waves for the original equation by appealing to the abstract theory of nonmonotone semiflows with asymptotic translation invariance. Further, we prove the stability and uniqueness of forced waves under appropriate conditions.