Food chain chaos due to Shilnikov's orbit

Bo Deng, Gwendolen Hines

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

Assume that the reproduction rate ratio ζ of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε0. The additional conditions under which such a singular orbit may occur are also explicitly given.

Original languageEnglish (US)
Pages (from-to)533-538
Number of pages6
JournalChaos
Volume12
Issue number3
DOIs
StatePublished - Sep 2002

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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