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Global stability and Neimark-Sacker bifurcation of a host-parasitoid model

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  • Qamar Din

Abstract

We investigate qualitative behaviour of a density-dependent discrete-time host-parasitoid model. Particularly, we study boundedness of solutions, existence and uniqueness of positive steady-state, local and global asymptotic stability of the unique positive equilibrium point and rate of convergence of modified host-parasitoid model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation with the help of bifurcation theory. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behaviour over a broad range of parameters. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the model.

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  • 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.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:6:p:1194-1202
    DOI: 10.1080/00207721.2016.1244308
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    References listed on IDEAS

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    1. Din, Q., 2014. "Global stability of a population model," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 119-128.
    2. Sun, Huijing & Cao, Hongjun, 2007. "Bifurcations and chaos of a delayed ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1383-1393.
    3. Zhang, Yue & Zhang, Qingling & Zhao, Lichun & Yang, Chunyu, 2007. "Dynamical behaviors and chaos control in a discrete functional response model," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1318-1327.
    4. Din, Qamar & Donchev, Tzanko, 2013. "Global character of a host-parasite model," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 1-7.
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    Cited by:

    1. 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).
    2. 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.
    3. Wei Yang, 2021. "Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay," Dynamic Games and Applications, Springer, vol. 11(4), pages 892-914, December.
    4. Zhu, Jianhua & Sun, Yanming, 2020. "Dynamic modeling and chaos control of sustainable integration of informatization and industrialization," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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