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Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

Author

Listed:
  • Miao Peng
  • Zhengdi Zhang
  • C. W. Lim
  • Xuedi Wang

Abstract

Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

Suggested Citation

  • Miao Peng & Zhengdi Zhang & C. W. Lim & Xuedi Wang, 2018. "Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:6052503
    DOI: 10.1155/2018/6052503
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    Cited by:

    1. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2021. "Interplay between epidemic and information spreading on multiplex networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 268-279.
    2. Tao, Xiangyu & Zhu, Linhe, 2021. "Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Zhu, Linhe & Huang, Xiaoyuan, 2021. "Modeling the dynamics of multi-cluster information propagation in presence of time delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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