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Complex dynamics in a food chain with slow and fast processes

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  • Jiang, Yongxin
  • Yang, Jianping

Abstract

This paper is devoted to the analysis of the dynamic behavior of a three-species food chain model, in which two predators compete for the same prey while one of the predators feeds on the other. Under the assumption that the time responses of the three trophic levels are extremely diversified, the model is proved to have homoclinic orbit. We firstly use geometric singular perturbation method to detect singular homoclinic orbits as well as parameter combinations for which these orbits exist. Then, we show, numerically, that there exist also nonsingular homoclinic orbits that tend toward the singular ones for slightly different parameter values. This analysis is particularly helpful to understanding the chaotic behavior of the food chains.

Suggested Citation

  • Jiang, Yongxin & Yang, Jianping, 2009. "Complex dynamics in a food chain with slow and fast processes," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3160-3168.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3160-3168
    DOI: 10.1016/j.chaos.2009.04.050
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    References listed on IDEAS

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    1. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. Wang, Fengyan & Pang, Guoping, 2008. "Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1366-1376.
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    Cited by:

    1. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.

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