Traveling waves of delayed reaction–diffusion systems with applications

Abstract The paper addresses the existence of traveling waves for n 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.

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