Stability of traveling wavefronts for a discrete diffusive competition system with three species

This paper is concerned with the nonlinear stability of monostable traveling wavefronts for a discrete three species competition diffusion system. Applying weighted energy method combining with the comparison principle, we first show that the traveling wavefronts with large speed are exponentially stable when the initial perturbation around the traveling wave decays exponentially as x→−∞ (but the initial perturbation can be arbitrarily large in other locations). Then, choosing different weight function, we improve the stability result to any traveling wavefronts with speed greater than the critical wave speed. We have to emphasize that the discrete dispersal operator in the system increases the difficulty of establishing energy estimates.