### 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 language | English (US) |
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Pages (from-to) | 514-525 |

Number of pages | 12 |

Journal | Chaos |

Volume | 11 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2001 |

### ASJC Scopus subject areas

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

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## Cite this

*Chaos*,

*11*(3), 514-525. https://doi.org/10.1063/1.1396340