Nonlinear stability of traveling wavefronts for competitive-cooperative Lotka-Volterra systems of three species

This paper is concerned with nonlinear stability of traveling wavefronts for competitive-cooperative Lotka-Volterra systems of three species. It is proved that all traveling wavefronts with speed c > c* are exponentially stable in L∞ space by the weighted energy method and comparison principle. Moreover, the time decay rates are obtained by weighted energy estimates.