IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v182y2024ics0960077924003862.html
   My bibliography  Save this article

Bifurcations of a Filippov ecological system with an A-type discontinuity boundary

Author

Listed:
  • Zhu, Yuxun
  • Zhang, Zhengdi
  • Ji, Jinchen

Abstract

Based on the integrated pest management strategy, this paper proposes a Filippov pest–natural enemy system with a novel threshold control strategy. We not only incorporate the changing rate into the control index of the pest population but also consider a threshold value for the natural enemy. This novel threshold policy presents the discontinuity boundary as a complicated ‘A’ type, which induces abundant and complex sliding dynamics. Through theoretical analysis, both curve boundaries could have at most six sliding segments and two pseudo-equilibria, while the other straight line boundary could have a unique stable sliding segment with two pseudo-equilibria. Numerically, the sliding mode bifurcation confirms that the system can have six sliding segments and two pseudo-equilibria simultaneously. Particularly, we discover a new global bifurcation phenomenon that may be termed as a triple limit cycle bifurcation, which reveals the coexistence of three nested limit cycles, various bistable states of two nested or independent attractors, as well as the appearance of a meaningful long transient. Our results not only demonstrate the important effect of nonlinear boundaries but also provide a new perspective on practical pest control problems.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003862
    DOI: 10.1016/j.chaos.2024.114834
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924003862
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.114834?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    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. 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).
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Jiao, Xubin & Liu, Xiuxiang, 2024. "Rich dynamics of a delayed Filippov avian-only influenza model with two-thresholds policy," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Li, Wenjie & Guan, Yajuan & Cao, Jinde & Xu, Fei, 2024. "Global dynamics and threshold control of a discontinuous fishery ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. 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.
    5. 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).
    6. 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).
    7. 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).
    8. 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.
    9. 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.
    10. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003862. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.