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Traveling waves in a diffusive predator-prey model with Holling type-III functional response. (English) Zbl 1155.37046

The authors establish the existence of travelling wave solutions and small amplitude travelling wave train solutions for a reaction-diffusion model based on a predator-prey system with a Holling type III functional response. The proof used the shooting argument, invariant manifold theory and Hopf bifurcation theorem. For simplicity It is assumed that the prey is not diffusive but this condition may be relaxed. This reviewer likes to add that Holling type III is useful in modeling the immune system hence the model studied in this paper may be used to model immune system-antigen interaction.

MSC:

37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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