Traveling wavefronts for a two-species ratio-dependent predator-prey system with diffusion terms and stage structure

Abstract In this paper, we considered an important nonlinear reaction-diffusion equations describing a two-species ratio-dependent predator–prey system with diffusion terms and stage structure. By using the linearized method, we investigated the locally asymptotical stability of the nonnegative equilibria of the above mentioned system and obtained the locally stable conditions. And by combining the approach introduced by J. Canosa (see [J. Canosa, On a nonlinear diffusion equation describing population growth, IBM J. Res. Deve. 17 (1973) 307–313]) with the method of upper and lower solutions, we proved that the traveling wavefronts which connect the zero solution with the positive constant equilibrium of the system exist and appear to be monotone. Finally, we gave a conclusion to summarize the achievements of the work.