Food chain chaos due to junction-fold point

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

Consideration is given to a basic food chain model satisfying the trophic time diversification hypothesis which translates the model into a singularly perturbed system of three time scales. It is demonstrated that in some realistic system parameter region, the model has a unimodal or logistic-like Poincaré return map when the singular parameter for the fastest variable is at the limiting value 0. It is also demonstrated that the unimodal map goes through a sequence of period-doubling bifurcations to chaos. The mechanism for the creation of the unimodal criticality is due to the existence of a junction-fold point [B. Deng, J. Math. Biol. 38, 21-78 (1999)]. The fact that junction-fold points are structurally stable and the limiting structures persist gives us a rigorous but dynamical explanation as to why basic food chain dynamics can be chaotic.

Original languageEnglish (US)
Pages (from-to)514-525
Number of pages12
JournalChaos
Volume11
Issue number3
DOIs
StatePublished - Sep 2001

ASJC Scopus subject areas

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

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