Bistable wavefronts of three-species competition-diffusion systems: Weak competition strategy between two species

This paper investigates the existence of wavefront solutions of the bistable Lotka-Volterra three-species competition-diffusion system. Due to the lack of the maximum principle, we first established the existence and asymptotic stability of traveling fronts for a simplified system without competition between two species. This simplified system exhibits the comparison principle. Subsequently, we utilize the heteroclinic bifurcation approach and perturbation theory of linearized operators to establish the existence and asymptotic stability of traveling fronts to the original system within specific parameter ranges in which the competition rates between the above two species are small enough. The monotone dependence of the wave speed on parameters is also discussed.