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Control of Hopf Bifurcation and Chaos in a Delayed Lotka‐Volterra Predator‐Prey System with Time‐Delayed Feedbacks

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  • Huitao Zhao
  • Yaowei Sun
  • Zhen Wang

Abstract

A delayed Lotka‐Volterra predator‐prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.

Suggested Citation

  • Huitao Zhao & Yaowei Sun & Zhen Wang, 2014. "Control of Hopf Bifurcation and Chaos in a Delayed Lotka‐Volterra Predator‐Prey System with Time‐Delayed Feedbacks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:104156
    DOI: 10.1155/2014/104156
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    References listed on IDEAS

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    1. Chen, Heng-Hui, 2009. "Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 466-473.
    2. El-Gohary, Awad & Al-Ruzaiza, A.S., 2007. "Chaos and adaptive control in two prey, one predator system with nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 443-453.
    3. Zhao, Huitao & Lin, Yiping, 2009. "Hopf bifurcation in a partial dependent predator–prey system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 896-900.
    4. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
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