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Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay

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  • Jiao, Xubin
  • Li, Xiaodi
  • Yang, Youping

Abstract

In this paper, the Leslie-Gower model with nonmonotonic functional response is extended to a nonsmooth Filippov control system to reflect the integrated pest management. Different from traditional Filippov models, here, we incorporate time delay as to account for predator maturity time. The stability of the equilibria and the existence of Hopf bifurcation of the subsystems are investigated. Moreover, sliding mode dynamics and regular/virtual/pseudoequilibria are analyzed. Numerical simulations indicate that all solutions finally converge to either the regular equilibrium, the pseudoequilibrium or a stable periodic solution according to different values of time delays and threshold levels. A boundary bifurcation that switches a stable regular equilibrium or a stable limit cycle to a stable pseudoequilibrium can occur. Meanwhile, global bifurcations from the standard periodic solution to the sliding switching bifurcation and then to the crossing bifurcation are obtained as time delay is increased. The results show that Filippov control strategies could effectively control the number of pests under the prescribed threshold, however, time delay may challenge pest control by the occurring of the sliding switching and crossing bifurcations.

Suggested Citation

  • Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006464
    DOI: 10.1016/j.chaos.2022.112436
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    References listed on IDEAS

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    1. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
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    3. Zhou, Hao & Tang, Sanyi, 2022. "Bifurcation dynamics on the sliding vector field of a Filippov ecological system," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    4. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
    5. Qin, Wenjie & Tan, Xuewen & Tosato, Marco & Liu, Xinzhi, 2019. "Threshold control strategy for a non-smooth Filippov ecosystem with group defense," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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