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Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control

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  • Xianghong Zhang
  • Sanyi Tang

Abstract

The Filippov ratio-dependent prey-predator model with economic threshold is proposed and studied. In particular, the sliding mode domain, sliding mode dynamics, and the existence of four types of equilibria and tangent points are investigated firstly. Further, the stability of pseudoequilibrium is addressed by using theoretical and numerical methods, and also the local sliding bifurcations including regular/virtual equilibrium bifurcations and boundary node bifurcations are studied. Finally, some global sliding bifurcations are addressed numerically. The globally stable touching cycle indicates that the density of pest population can be successfully maintained below the economic threshold level by designing suitable threshold policy strategies.

Suggested Citation

  • Xianghong Zhang & Sanyi Tang, 2013. "Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    • Handle: RePEc:hin:jnlaaa:280945
    DOI: 10.1155/2013/280945
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    Cited by:

    1. Lirong Liu & Changcheng Xiang & Guangyao Tang & Yuan Fu, 2019. "Sliding Dynamics of a Filippov Forest-Pest Model with Threshold Policy Control," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    2. Li, Wenxiu & Chen, Yuming & Huang, Lihong & Wang, Jiafu, 2022. "Global dynamics of a filippov predator-prey model with two thresholds for integrated pest management," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Pei, Yongzhen & Shen, Na & Zhao, Jingjing & Yu, Yuping & Chen, Yasong, 2023. "Analysis and simulation of a delayed HIV model with reaction–diffusion and sliding control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 382-405.

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