Nonlinear Dynamics

, Volume 69, Issue 1–2, pp 275–284 | Cite as

Hopf bifurcation and chaos in fractional-order modified hybrid optical system

  • Mohammed-Salah Abdelouahab
  • Nasr-Eddine Hamri
  • Junwei Wang
Original Paper


In this paper, a chaotic fractional-order modified hybrid optical system is presented. Some basic dynamical properties are further investigated by means of Poincaré mapping, parameter phase portraits, and the largest Lyapunov exponents. Fractional Hopf bifurcation conditions are proposed; it is found that Hopf bifurcation occurs on the proposed system when the fractional-order varies and passes a sequence of critical values. The chaotic motion is validated by the positive Lyapunov exponent. Finally, some numerical simulations are also carried out to illustrate our results.


Fractional system Stability Hopf bifurcation Chaos 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Mohammed-Salah Abdelouahab
    • 1
  • Nasr-Eddine Hamri
    • 1
  • Junwei Wang
    • 2
  1. 1.Institute of Science and TechnologyUniversity Center of MilaMilaAlgeria
  2. 2.Cisco School of InformaticsGuangdong University of Foreign StudiesGuangzhouP.R. China

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