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Dynamical behaviors and chaos control in a discrete functional response model

Author

Listed:
  • Zhang, Yue
  • Zhang, Qingling
  • Zhao, Lichun
  • Yang, Chunyu

Abstract

In this paper, the dynamical behaviors and chaos control are investigated in a discrete functional response model. It is verified that there are phenomena of the transcritical bifurcation, flip bifurcation, Hopf bifurcation types and chaos in the sense of Marotto’s definition. Specifically, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one (i.e., an unstable fixed point of the chaotic system). Finally, numerical simulations not only show the consistency with theoretical analysis but also exhibit the complex dynamical behaviors.

Suggested Citation

  • Zhang, Yue & Zhang, Qingling & Zhao, Lichun & Yang, Chunyu, 2007. "Dynamical behaviors and chaos control in a discrete functional response model," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1318-1327.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1318-1327
    DOI: 10.1016/j.chaos.2006.04.032
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    Cited by:

    1. Qamar Din, 2017. "Global stability and Neimark-Sacker bifurcation of a host-parasitoid model," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(6), pages 1194-1202, April.
    2. Goharrizi, Amin Yazdanpanah & Khaki-Sedigh, Ali & Sepehri, Nariman, 2009. "Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2448-2455.
    3. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.

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