Chaos and Hopf bifurcation control in a fractional-order memristor-based chaotic system with time delay

  • Dawei Ding
  • Xin Qian
  • Wei Hu
  • Nian Wang
  • Dong Liang
Regular Article
  • 58 Downloads

Abstract.

In this paper, a time-delayed feedback controller is proposed in order to control chaos and Hopf bifurcation in a fractional-order memristor-based chaotic system with time delay. The associated characteristic equation is established by regarding the time delay as a bifurcation parameter. A set of conditions which ensure the existence of the Hopf bifurcation are gained by analyzing the corresponding characteristic equation. Then, we discuss the influence of feedback gain on the critical value of fractional order and time delay in the controlled system. Theoretical analysis shows that the controller is effective in delaying the Hopf bifurcation critical value via decreasing the feedback gain. Finally, some numerical simulations are presented to prove the validity of our theoretical analysis and confirm that the time-delayed feedback controller is valid in controlling chaos and Hopf bifurcation in the fractional-order memristor-based system.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Dawei Ding
    • 1
    • 2
  • Xin Qian
    • 2
  • Wei Hu
    • 2
  • Nian Wang
    • 1
    • 2
  • Dong Liang
    • 1
    • 2
  1. 1.Key Laboratory of Intelligent Computing and Signal Processing, Ministry of EducationAnhui UniversityHefeiChina
  2. 2.School of Electronics and Information EngineeringAnhui UniversityHefeiChina

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