Travelling wave and global attractivity in a competition–diffusion system with nonlocal delays

In this paper, we are concerned with a two-competition model described by a reaction–diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times. By using the iterative technique recently developed in Wang et al. (2006) [14], the sufficient conditions are established for the existence of travelling wave solutions connecting the semi-trivial steady state to the coexistence steady state of the considered system. When the domain is bounded, we investigate the global attractivity of the coexistence steady state of the system under homogeneous Neumann boundary conditions as well. The approach used is the upper–lower solutions and monotone iteration technique.