Stability of travelling wave solutions of diffusive predator-prey systems

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Stability of Travelling Wave Solutions of Diffusive Predator - Prey Systems

The stability of travelling wave solutions of singularly perturbed, diffusive predator-prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue at k 0 is simple. The proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues.

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Existence of traveling wave solutions for diffusive predator–prey type systems

Article history: Received 21 September 2010 Revised 18 October 2011 Available online 30 November 2011

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

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...

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1991

ISSN: 0002-9947,1088-6850

DOI: 10.1090/s0002-9947-1991-1013331-0