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

Cheng Hsiung Hsu, Chi Ru Yang, Ting Hui Yang, Tzi Sheng Yang

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Abstract

In this work we investigate the existence of traveling wave solutions for a class of diffusive predator-prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle's Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.

Original languageEnglish
Pages (from-to)3040-3075
Number of pages36
JournalJournal of Differential Equations
Volume252
Issue number4
DOIs
StatePublished - 15 Feb 2012

Keywords

  • Hopf bifurcation theory
  • LaSalle's invariance Principle
  • Lyapunov function
  • Predator-prey
  • Traveling wave
  • Wazewski theorem

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