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Global dynamics of a filippov predator-prey model with two thresholds for integrated pest management

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  • Li, Wenxiu
  • Chen, Yuming
  • Huang, Lihong
  • Wang, Jiafu

Abstract

Based on the integrated pest management strategy, we propose and analyze a Filippov predator-prey model. Different from existing works, the feature of the model is that two thresholds are involved, one (xT) for pest and the other (yT) for natural enemy. We distinguish three cases according to the value of xT. Then we classify the dynamics for each case considering the relationship of the levels of the natural enemy at equilibria to yT by applying Filippov theory. Specifically, we investigate the sliding mode dynamics and global dynamics. It is shown that, for different parameter values, the proposed system can admit coexistence of multi-attractors including a real equilibrium, a pseudo-equilibrium, and a pseudo-attractor (xT,yT). These theoretical results are also illustrated with numerical simulations. Our findings indicate that proper control strategies can prevent the outbreak of pest disaster in ecological agriculture.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000923
    DOI: 10.1016/j.chaos.2022.111881
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    References listed on IDEAS

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    1. Li, Wenxiu & Huang, Lihong & Wang, Jiafu, 2021. "Global asymptotical stability and sliding bifurcation analysis of a general Filippov-type predator-prey model with a refuge," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. 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.
    3. Tang, Guangyao & Qin, Wenjie & Tang, Sanyi, 2014. "Complex dynamics and switching transients in periodically forced Filippov prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 13-23.
    4. 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.
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    Cited by:

    1. Airen Zhou, 2023. "Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions," Mathematics, MDPI, vol. 11(13), pages 1-18, July.
    2. Dong, Cunjuan & Xiang, Changcheng & Xiang, Zhongyi & Yang, Yi, 2022. "Global dynamics of a Filippov epidemic system with nonlinear thresholds," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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