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Qualitative analysis and control for predator-prey delays system

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  • Chen, Xiaoxiao
  • Wang, Xuedi

Abstract

In this paper, the dynamics of a stage-structured predator-prey system with two time delays and Monod–Haldane response function are considered. By taking the two time delays as the bifurcation parameter, the local stability of the interior equilibrium is established and the conditions for existence of the Hopf bifurcation are obtained. Furthermore, based on the normal form method and center manifold theorem, the direction of the Hopf bifurcation and the stability of the bifurcation period solutions are investigated. In addition, by using parameter disturbance and state feedback control to act on the system, we succeeded in controlling the Hopf bifurcation of the original system. Numerical examples are given to carry out to support the obtained theoretical findings.

Suggested Citation

  • Chen, Xiaoxiao & Wang, Xuedi, 2019. "Qualitative analysis and control for predator-prey delays system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 361-372.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:361-372
    DOI: 10.1016/j.chaos.2019.04.023
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    References listed on IDEAS

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    1. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    2. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
    3. Wang, Xuedi & Peng, Miao & Liu, Xiuyu, 2015. "Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 496-508.
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    Cited by:

    1. Wang, Jingnan & Shi, Hongbin & Xu, Li & Zang, Lu, 2022. "Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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