IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n963072.html

Geometric Analysis of an Integrated Pest Management Model Including Two State Impulses

Author

Listed:
  • Wencai Zhao
  • Yulin Liu
  • Tongqian Zhang
  • Xinzhu Meng

Abstract

According to integrated pest management strategies, we construct and investigate the dynamics of a Holling‐Tanner predator‐prey system with state dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Applying the Dulacs criterion, the global stability of the positive equilibrium in the system without impulsive effect is discussed. By using impulsive differential equation geometry theory and the method of successor functions, we prove the existence of periodic solution of the system with state dependent impulsive effects. Furthermore, the stability conditions of periodic solutions are obtained. Some simulations are exerted to illustrate the feasibility of our main results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:963072
    DOI: 10.1155/2014/963072
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/963072
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/963072?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. Chunjin Wei & Lansun Chen, 2012. "Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, November.
    3. Chunjin Wei & Lansun Chen, 2012. "Periodic Solution of Prey‐Predator Model with Beddington‐DeAngelis Functional Response and Impulsive State Feedback Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(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. Neslihan Nesliye Pelen & Ayşe Feza Güvenilir & Billur Kaymakçalan, 2016. "Behavior of the Solutions for Predator‐Prey Dynamic Systems with Beddington‐DeAngelis Type Functional Response on Periodic Time Scales in Shifts," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. Zhang, Meng & Zhao, Yi & Chen, Lansun & Li, Zeyu, 2020. "State feedback impulsive modeling and dynamic analysis of ecological balance in aquaculture water with nutritional utilization rate," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    8. Liu, Qiong & Zhang, Meng & Chen, Lansun, 2019. "State feedback impulsive therapy to SIS model of animal infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 222-232.
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. 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.
    16. 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.
    17. Jiménez, María Fernanda & Blé, Gamaliel & Falconi, Manuel, 2022. "A biocontrol agent as a commensal in a plant-pest interaction," Ecological Modelling, Elsevier, vol. 468(C).

    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:jnlaaa:v:2014:y:2014:i:1:n:963072. 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/4058 .

    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.