Springfield: American Institute of Mathematical Sciences
In this paper, we shall survey some recent results on the wave propagation in 2-species competition systems with Lotka-Volterra type non- linearity. This includes systems with continuous and discrete diffusion (or migration). We are interested in both monostable case and bistable with strong competition case. Questions on minimal speed for the monostable case, uniqueness of wave speed and propagation failure in the bistable case, monotonicity and uniqueness of wave profile for both cases are addressed. Finally, we give some open problems on wave propagation in 2-species competition systems.
Discrete & Continuous Dynamical Systems - Series B 17(8), pp.2713-2724