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Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy

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  • Wang, Weiming
  • Wang, Xiaoqin
  • Lin, Yezhi

Abstract

Based on the classical predator–prey system with Watt-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator at different fixed time for pest control is proposed and investigated. It proves that there exists a globally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, and otherwise, the system can be permanent. Numerical results show that the system considered has more complicated dynamics involving quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and “crises”, etc. It will be useful for studying the dynamic complexity of ecosystems.

Suggested Citation

  • Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1427-1441
    DOI: 10.1016/j.chaos.2006.10.032
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    1. Kim, Hye Kyung & Baek, Hunki, 2013. "The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 1-14.

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