Hybrid control of delay induced hopf bifurcation of dynamical small-world network



In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay. With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis.

Key words

Hopf bifurcation hybrid control small-world network bifurcation control 

CLC number

O 193 

Document code


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Copyright information

© Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Dawei Ding (丁大为)
    • 1
    • 2
  • Xiaoyun Zhang (张肖芸)
    • 2
  • Nian Wang (王 年)
    • 1
    • 2
  • Dong Liang (梁 栋)
    • 1
    • 2
  1. 1.Key Laboratory of Intelligent Computing and Signal Processing of Ministry of EducationHefeiChina
  2. 2.School of Electronics and Information EngineeringAnhui UniversityHefeiChina

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