Food chain chaos due to Shilnikov's orbit

Bo Deng, Gwendolen Hines

Research output: Contribution to journalArticle

45 Citations (Scopus)

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

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food chain
Food Chain
predators
Predator
Chaos theory
chaos
Chaos
Orbits
Orbit
orbits
Food Chain Model
Singularly Perturbed Systems
Singular Limit
Homoclinic Orbit
saddles
Saddle
Prey
Time Scales
Model

ASJC Scopus subject areas

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

Cite this

Food chain chaos due to Shilnikov's orbit. / Deng, Bo; Hines, Gwendolen.

In: Chaos, Vol. 12, No. 3, 09.2002, p. 533-538.

Research output: Contribution to journalArticle

Deng, Bo ; Hines, Gwendolen. / Food chain chaos due to Shilnikov's orbit. In: Chaos. 2002 ; Vol. 12, No. 3. pp. 533-538.
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