Food chain chaos due to transcritical point

Bo Deng, Gwendolen Hines

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincaré map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincaré map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.

Original languageEnglish (US)
Pages (from-to)578-585
Number of pages8
Issue number2
StatePublished - Jun 2003

ASJC Scopus subject areas

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

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