Traveling waves of delayed reaction–diffusion systems with applications

The paper addresses the existence of traveling waves for nn components delayed reaction–diffusion systems with the weak quasi-monotonicity or the weak exponential quasi-monotonicity. The approach is based on a cross iteration scheme combining Schauder’s fixed point theorem for the corresponding wave profile systems. The results are well applied to a three-species competitive Lotka–Volterra reaction–diffusion system with multiple delays. The existence of traveling waves which connects the trivial equilibrium and the positive equilibrium indicates that there is a transition zone moving the steady state with no species to the steady state with the coexistence of three species.