Topological horseshoes of traveling waves for a fast-slow predator-prey system

Marcio Gameiro, Tomáš Gedeon, William Kalies, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We show the existence of a set of periodic traveling waves in a system of two scalar reaction diffusion equations, which is in one-to-one correspondence with a full shift on two symbols. We use a novel combination of rigorous numerical computations and the topological techniques of the Conley index theory. This approach is quite general, and this paper is intended as a demonstration of its usefulness and applicability.

Original languageEnglish (US)
Pages (from-to)623-654
Number of pages32
JournalJournal of Dynamics and Differential Equations
Issue number3
StatePublished - Sep 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis


  • Conley index theory
  • Predator-prey system
  • Rigorous computation
  • Singular perturbation
  • Symbolic dynamics
  • Traveling wave


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