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On Hopf bifurcation and control for a delay systems

Author

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  • Jiang, Xiaowei
  • Chen, Xiangyong
  • Chi, Ming
  • Chen, Jie

Abstract

Hopf bifurcation of a delay differential equation modeling two-enterprise interaction mechanism is investigated. For the demands of computer simulation applications, the discrete-time two-enterprise interaction model is proposed by using the forward Euler scheme. By discussing the characteristic equation of linearized part, the local stability criterion of the positive fixed point is presented. Time lag is selected as the bifurcation parameter. Then it is demonstrated that variation of time lag may result in Hopf bifurcation. Furthermore, derivations for the directions and stability of Hopf bifurcation are also given. For the purpose of controlling Hopf bifurcation, a time-delayed feedback control scheme is proposed. Finally, we simulate the main results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319308987
    DOI: 10.1016/j.amc.2019.124906
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    References listed on IDEAS

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    1. Tang, Xiaosong & Song, Yongli, 2015. "Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator–prey model with herd behavior," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 375-391.
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    5. Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
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    Cited by:

    1. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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