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Hybrid control of bifurcation in a predator-prey system with three delays

Zhang Li-Ping Wang Hui-Nan Xu Min

Hybrid control of bifurcation in a predator-prey system with three delays

Zhang Li-Ping, Wang Hui-Nan, Xu Min
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Publishing process
  • Received Date:  06 August 2008
  • Accepted Date:  24 June 2010
  • Published Online:  15 January 2011

Hybrid control of bifurcation in a predator-prey system with three delays

  • 1. (1)College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;Collge of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; (2)Collge of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; (3)Collge of Information Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Abstract: The problem of Hopf bifurcation control for a predator-prey system with three delays is considered. A new hybrid strategy is proposed to control the Hopf bifurcation, in which the state feedback and parameter perturbation are used to delay the onset of an inherent bifurcation or make the bifurcation disappear. The stability and the existence of bifurcation are researched. In particular, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form theory and center manifold theorem. Finally, numerical simulation results confirm that the new hybrid controller is efficient in controlling Hopf bifurcation.

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