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Applications of chaos control techniques to a three-species food chain

Author

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  • Gomes, A.A.
  • Manica, E.
  • Varriale, M.C.

Abstract

We achieve control of deterministic chaos in an ecosystem model, involving three first-order nonlinear differential equations with a control parameter, recently proposed by Hastings and Powell (HP) in order to describe the dynamical behavior of a three-species food chain. After identifying a chaotic attractor corresponding to a particular value of the parameter of this ecological model, we locate periodic saddle orbits embedded in it. By applying the Ott–Grebogi–Yorke (OGY) method of controlling chaos, which introduces small time-dependent perturbations on the system parameter, we stabilize two of the saddle orbits. Furthermore, we check the versatility of the OGY method, as the system behavior is allowed to switch between ‘no control’ and ‘control’ about one or other of different stabilized periodic orbits.

Suggested Citation

  • Gomes, A.A. & Manica, E. & Varriale, M.C., 2008. "Applications of chaos control techniques to a three-species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 432-441.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:432-441
    DOI: 10.1016/j.chaos.2006.05.075
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    Cited by:

    1. Zhao, Min & Yu, Hengguo & Zhu, Jun, 2009. "Effects of a population floor on the persistence of chaos in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1245-1250.
    2. Sun, Chengjun & Loreau, Michel, 2009. "Dynamics of a three-species food chain model with adaptive traits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2812-2819.

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