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Travelling waves in predator-prey systems. (English) Zbl 0815.35045

Summary: The existence of travelling wave solutions to reaction-diffusion equations which model predator-prey systems is proven. Bistable waves, Fisher waves, and higher-dimensional analogues of Fisher waves are found. Some of the systems investigated have bistable homoclinic waves. The proofs use the Conley index, continuation, the connection matrix, and bifurcation theory in the Conley index setting.

MSC:

35K57 Reaction-diffusion equations
35K45 Initial value problems for second-order parabolic systems
35B32 Bifurcations in context of PDEs
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