The propagation dynamics for three species competitive-cooperative reaction–diffusion systems

This paper is concerned with the sign of bistable wave speed and spreading properties of solutions for a class of three species competitive-cooperative reaction–diffusion systems. We establish sufficient conditions for a species to be the winner, which also extends the known results for two-species Loltka–Volterra competition model. Then we show that the species with large invasion speed can always establish a wave moving into open space with its own speed, while the others will be driven out or invade successfully, depending on the parameters, at a lower speed.