Traveling waves for n-species competitive system with nonlocal dispersals and delays

• n-species competitive system with nonlocal dispersals is investigated.
• The abstract results are developed for more general nonlocal systems.
• Existence of traveling waves is obtained by using the developed abstract result.
• Numerical simulations are carried out to illustrate the main results.

This paper is concerned with traveling waves for n-species competitive Lotka–Volterra system with nonlocal dispersals and delays. Existence of traveling waves which connect 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 n-species. In order to obtain the result, we first investigate the general theory for the general systems with the nonlocal dispersals by using Schauder’s fixed point theorem. Numerical simulations are carried out to illustrate the main theoretical results. The work obtained can be seen as a generalization of previous results.