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Existence of traveling wave solutions in a diffusive predator-prey model. (English) Zbl 1018.92026

Summary: 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 \(R^4\) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in \(R^4\). The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.

MSC:

92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
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