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Threshold control strategy for a non-smooth Filippov ecosystem with group defense

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  • Qin, Wenjie
  • Tan, Xuewen
  • Tosato, Marco
  • Liu, Xinzhi

Abstract

A non-smooth Filippov ecosystem with group defense is proposed to investigate the effects of threshold and intermittent control strategy for IPM. The proposed model has been analyzed theoretically using the qualitative analysis techniques related to Filippov non-smooth systems in the first place. In particular, the existence and stability of equilibria are discussed for the sliding mode dynamics, through which it can be shown that the real equilibrium and pseudo-equilibrium can coexist. After that, some relevant topics such as sliding mode bifurcation, boundary-focus bifurcation, grazing bifurcation, crossing bifurcation and buckling bifurcation are investigated using numerical analysis. These complex sliding bifurcations reveal that the proposed Filippov system admits the coexistence of multi-attractors including equilibrium and crossing cycles, thus indicating that there exists a close relationship between the intermittent control strategy and the initial densities of both populations. Similarly, the global stability properties of real equilibrium and pseudo-equilibrium of subsystems show that the intermittent control strategy can effectively control the pests under the prescribed threshold which is the aim of the IPM strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:15
    DOI: 10.1016/j.amc.2019.06.046
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    References listed on IDEAS

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    1. Qin, Wenjie & Tang, Sanyi & Xiang, Changcheng & Yang, Yali, 2016. "Effects of limited medical resource on a Filippov infectious disease model induced by selection pressure," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 339-354.
    2. Falconi, Manuel & Huenchucona, Marcelo & Vidal, Claudio, 2015. "Stability and global dynamic of a stage-structured predator–prey model with group defense mechanism of the prey," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 47-61.
    3. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
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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. 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).
    3. Zhang, Hongxia & Han, Ping & Guo, Qin, 2023. "Stability and jumping dynamics of a stochastic vegetation ecosystem induced by threshold policy control," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Zhu, Yuxun & Zhang, Zhengdi & Ji, Jinchen, 2024. "Bifurcations of a Filippov ecological system with an A-type discontinuity boundary," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. 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).
    6. 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).
    7. Wenjie Qin & Zhengjun Dong & Lidong Huang, 2024. "Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies," Mathematics, MDPI, vol. 12(7), pages 1-25, March.

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