Traveling Wavefronts For Competitive Lotka-volterra Systems With Nonlocal Terms

In this paper,we study the existence and stability of traveling wavefronts of non-local competitive Lotka-Volterra systems with weak and strong kernel functions for competition between species with different mobility and diffusion abilities.For the existence of the traveling wavefronts,the upper and lower solution method and the Schauder fixed point theorem are mainly applied.Furthermore,we transform the problem into the existence of a pair of upper and lower solutions that satisfy some appropriate conditions.Therefore,we firstly construct a pair of upper and lower solutions by using the monotone iterative method,and then prove the existence of the traveling wavefronts of the system by verifying the corresponding conditions.Moreover,we prove the asymptotic behavior of the traveling wavefronts at negative infinity.For the stability analysis of the traveling wavefronts,we obtain the instability of the traveling wavefronts in uniformly continuous function space by applying the spectral analysis method of linear operators,and obtain the asymptotic stability of the traveling wavefronts with non-critical wave velocity when the initial perturbation of the traveling wavefronts is limited to a certain exponentially weighted space.Finally,we draw a conclusion that the species with stronger competitiveness always win the competition and persist in species competition.However,the species with weaker competitiveness are likely to change from the initial competitive advantage to the final disadvantage and then to be eliminated by the environment,whether it has the same spatial mobility as the species with stronger competitiveness or stronger spatial mobility.