IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6509867.html
   My bibliography  Save this article

The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate

Author

Listed:
  • Ihsan Ullah Khan
  • Sanyi Tang
  • Biao Tang

Abstract

Whether the integrated control measures are applied or not depends not only on the current density of pest population, but also on its current growth rate, and this undoubtedly brings challenges and new ideas to the state control measures that only rely on the pest density. To address this, utilizing the tactics of IPM, we constructed a Lotka-Volterra predator-prey system with action threshold depending on the pest density and its changing rate and examined its dynamical behavior. We present new criteria guaranteeing the existence, uniqueness, and global stability of periodic solutions. With the help of Lambert W function, the Poincaré map is constructed for the phase set, which can help us to provide the satisfactory conditions for the existence and stability of the semitrivial periodic solution and interior order-1 periodic solutions. Furthermore, the existence of order-2 and nonexistence of order- periodic solutions are discussed. The idea of action threshold depending on the pest density and its changing rate is more general and can generate new remarkable directions as well compared with those represented in earlier studies. The analytical techniques developed in this paper can play a significant role in analyzing the impulsive models with complex phase set or impulsive set.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:6509867
    DOI: 10.1155/2019/6509867
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/6509867.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/6509867.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6509867?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. Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    2. Xiao, Qizhen & Dai, Binxiang, 2015. "Dynamics of an impulsive predator–prey logistic population model with state-dependent," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 220-230.
    3. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    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. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.
    3. 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.
    4. Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Jiang, Fangfang & Sun, Jitao, 2016. "On the existence of discontinuous periodic solutions for a class of Liénard systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 259-265.
    6. Liu, Yanwei & Zhang, Tonghua & Liu, Xia, 2020. "Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.
    8. 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.
    9. Toni Bakhtiar & Ihza Rizkia Fitri & Farida Hanum & Ali Kusnanto, 2022. "Mathematical Model of Pest Control Using Different Release Rates of Sterile Insects and Natural Enemies," Mathematics, MDPI, vol. 10(6), pages 1-18, March.
    10. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    11. Li, Hongjie & Zhu, Yinglian & jing, Liu & ying, Wang, 2018. "Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 1-15.
    12. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    13. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
    14. Qi Cai & Yushi Cai & Yali Wen, 2018. "Spatially Differentiated Trends between Forest Pest-Induced Losses and Measures for Their Control in China," Sustainability, MDPI, vol. 11(1), pages 1-16, December.
    15. Bor-Sen Chen & Xiangyun Lin & Weihai Zhang & Tianshou Zhou, 2018. "On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    16. Li, Qian & Liu, Xinzhi & Zhu, Qingxin & Zhong, Shouming & Zhang, Dian, 2019. "Distributed state estimation for stochastic discrete-time sensor networks with redundant channels," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 230-246.
    17. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    18. Zhenzhen Shi & Yaning Li & Huidong Cheng, 2019. "Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay," Mathematics, MDPI, vol. 7(7), pages 1-15, July.
    19. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    20. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.

    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:hin:complx:6509867. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.