### 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) |
---|---|

Pages (from-to) | 514-525 |

Number of pages | 12 |

Journal | Chaos |

Volume | 11 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2001 |

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### ASJC Scopus subject areas

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

### Cite this

*Chaos*,

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

**Food chain chaos due to junction-fold point.** / Deng, Bo.

Research output: Contribution to journal › Article

*Chaos*, vol. 11, no. 3, pp. 514-525. https://doi.org/10.1063/1.1396340

}

TY - JOUR

T1 - Food chain chaos due to junction-fold point

AU - Deng, Bo

PY - 2001/9

Y1 - 2001/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035458186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035458186&partnerID=8YFLogxK

U2 - 10.1063/1.1396340

DO - 10.1063/1.1396340

M3 - Article

C2 - 12779489

AN - SCOPUS:0035458186

VL - 11

SP - 514

EP - 525

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 3

ER -