IDEAS home Printed from https://ideas.repec.org/a/wly/complx/v2022y2022i1n7903450.html

A State‐Dependent Impulsive Nonlinear System with Ratio‐Dependent Action Threshold for Investigating the Pest‐Natural Enemy Model

Author

Listed:
  • Ihsan Ullah Khan
  • Saif Ullah
  • Ebenezer Bonyah
  • Basem Al Alwan
  • Ahmed Alshehri

Abstract

Based on the Lotka–Volterra system, a pest‐natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending on the density of real‐time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order‐1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state‐dependent feedback control models.

Suggested Citation

  • Ihsan Ullah Khan & Saif Ullah & Ebenezer Bonyah & Basem Al Alwan & Ahmed Alshehri, 2022. "A State‐Dependent Impulsive Nonlinear System with Ratio‐Dependent Action Threshold for Investigating the Pest‐Natural Enemy Model," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:7903450
    DOI: 10.1155/2022/7903450
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/7903450
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/7903450?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
    ---><---

    References listed on IDEAS

    as
    1. Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2008. "Multiple attractors of host–parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak," Theoretical Population Biology, Elsevier, vol. 73(2), pages 181-197.
    2. Gritli, Hassène & Belghith, Safya, 2017. "Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Analysis of local bifurcations via the hybrid Poincaré map," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 72-87.
    3. Znegui, Wafa & Gritli, Hassène & Belghith, Safya, 2020. "Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Ihsan Ullah Khan & Sanyi Tang & Biao Tang, 2019. "The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate," Complexity, Hindawi, vol. 2019, pages 1-15, June.
    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. Mohammad Sajid, 2020. "Chaotic Behaviour and Bifurcation in Real Dynamics of Two‐Parameter Family of Functions including Logarithmic Map," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    2. Gao, Jinfeng & Tan, Zhonghao & Li, Lebao & Jia, Guoqiang & Liu, Peter Xiaoping, 2025. "A novel finite-time non-singular robust control for robotic manipulators," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    3. Jiang, Bo & Jiang, Hui & Liu, Qihuai & Jiang, Guirong, 2024. "Periodic gait classification and control of a biped model with telescopic legs and pulse thrust," Chaos, Solitons & Fractals, Elsevier, vol. 183(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. Gritli, Hassène & Belghith, Safya, 2018. "Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Rise of the Neimark–Sacker bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 158-168.
    6. Yang, Jin & Tang, Sanyi & Tan, Yuanshun, 2016. "Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 522-532.
    7. Liang, Juhua & Tang, Sanyi & Cheke, Robert A., 2016. "Pure Bt-crop and mixed seed sowing strategies for optimal economic profit in the face of pest resistance to pesticides and Bt-corn," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 6-21.
    8. Znegui, Wafa & Gritli, Hassène & Belghith, Safya, 2020. "Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Cheng, Huidong & Li, Wei & Zhang, Tonghua, 2024. "Complex dynamic analysis of a big fish-small fish system by using the Poincaré map," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    10. Rao, XiaoBo & Gao, JianShe & Ding, ShunLiang & Liang, Jie & Zhang, Jiangang, 2023. "Multistability of gaits, the basin of attraction and its external topology in the simplest passive walking model on stairs," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    11. Peipei Wang & Wenjie Qin & Guangyao Tang, 2019. "Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    12. Tao Wang & Youtang Zhang, 2016. "Chemical Control for Host‐Parasitoid Model within the Parasitism Season and Its Complex Dynamics," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    13. Gritli, Hassène, 2019. "Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 127-145.
    14. Wang, Xia & Xu, Zihui & Tang, Sanyi & Cheke, Robert A., 2017. "Cumulative effects of incorrect use of pesticides can lead to catastrophic outbreaks of pests," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 7-19.
    15. Xiang, Zhongyi & Tang, Sanyi & Xiang, Changcheng & Wu, Jianhong, 2015. "On impulsive pest control using integrated intervention strategies," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 930-946.
    16. Changcheng Xiang & Zhongyi Xiang & Yi Yang, 2014. "Dynamic Complexity of a Switched Host‐Parasitoid Model with Beverton‐Holt Growth Concerning Integrated Pest Management," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    17. Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2010. "Dynamical analysis of plant disease models with cultural control strategies and economic thresholds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 894-921.
    18. Wencai Zhao & Yulin Liu & Tongqian Zhang & Xinzhu Meng, 2014. "Geometric Analysis of an Integrated Pest Management Model Including Two State Impulses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    19. 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.
    20. Zhao, Tingting & Xiao, Yanni, 2015. "Plant disease models with nonlinear impulsive cultural control strategies for vegetatively propagated plants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 61-91.

    More about this item

    Statistics

    Access and download statistics

    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:wly:complx:v:2022:y:2022:i:1:n:7903450. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/8503 .

    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.