IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p536-d341585.html
   My bibliography  Save this article

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Author

Listed:
  • Xiaorong Ma

    (Office of School Enterprise Cooperation and Innovation and Entrepreneurship Education, Shaanxi Vocational and Technical College, Xi’an 710038, China)

  • Qamar Din

    (Department of Mathematics, The University of Poonch Rawalakot, Azad Kashmir 10250, Pakistan)

  • Muhammad Rafaqat

    (Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan)

  • Nasir Javaid

    (Abdus Salam School of Mathematical Sciences, Lahore 54000, Pakistan)

  • Yongliang Feng

    (School of information Engineering, Xi’an University, Xi’an 710065, China)

Abstract

The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.

Suggested Citation

  • Xiaorong Ma & Qamar Din & Muhammad Rafaqat & Nasir Javaid & Yongliang Feng, 2020. "A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control," Mathematics, MDPI, vol. 8(4), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:536-:d:341585
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/536/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/536/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Qamar Din, 2017. "Global stability and Neimark-Sacker bifurcation of a host-parasitoid model," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(6), pages 1194-1202, April.
    2. Jianming Zhang & Lijun Zhang & Yuzhen Bai, 2019. "Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    3. Xu, Cailin & Boyce, Mark S., 2005. "Dynamic complexities in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 175-182.
    4. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a host–parasitoid model with a lower bound for the host," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 911-919.
    5. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
    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. Zhang, Limin & Zhao, Min, 2009. "Dynamic complexities in a hyperparasitic system with prolonged diapause for host," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1136-1142.
    2. Zhu, Lili & Zhao, Min, 2009. "Dynamic complexity of a host–parasitoid ecological model with the Hassell growth function for the host," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1259-1269.
    3. Yousef, A.M. & Rida, S.Z. & Ali, H.M. & Zaki, A.S., 2023. "Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Lv, Songjuan & Fang, Zhongmiao, 2009. "The dynamic complexity of a host–parasitoid model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2617-2623.
    5. Jiang, Xiaowei & Chen, Xiangyong & Chi, Ming & Chen, Jie, 2020. "On Hopf bifurcation and control for a delay systems," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    6. Binhao Hong & Chunrui Zhang, 2023. "Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    7. Yu, Hengguo & Zhao, Min & Lv, Songjuan & Zhu, Lili, 2009. "Dynamic complexities in a parasitoid-host-parasitoid ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 39-48.
    8. Zhong, Shihong & Xia, Juandi & Liu, Biao, 2021. "Spatiotemporal dynamics analysis of a semi-discrete reaction-diffusion Mussel-Algae system with advection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Akhtar, S. & Ahmed, R. & Batool, M. & Shah, Nehad Ali & Chung, Jae Dong, 2021. "Stability, bifurcation and chaos control of a discretized Leslie prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    11. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    12. Ali Yousef & Fatma Bozkurt Yousef, 2019. "Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    13. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Xiongxiong Du & Xiaoling Han & Ceyu Lei, 2022. "Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    15. Zhu, Jianhua & Sun, Yanming, 2020. "Dynamic modeling and chaos control of sustainable integration of informatization and industrialization," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    16. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    17. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a host–parasitoid model with a lower bound for the host," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 911-919.
    19. Zhao, Min & Yu, Hengguo & Zhu, Jun, 2009. "Effects of a population floor on the persistence of chaos in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1245-1250.
    20. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.

    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:gam:jmathe:v:8:y:2020:i:4:p:536-:d:341585. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.