Existence of traveling wave solutions in a diffusive predator-prey model

Abstract We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R4 and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R4. The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.

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