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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
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
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