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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Science and Technology, University Center of Mila, Mila, 43000, Algeria

    Mohammed-Salah Abdelouahab & Nasr-Eddine Hamri

  2. Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou, 510006, P.R. China

    Junwei Wang

Authors
  1. Mohammed-Salah Abdelouahab
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  2. Nasr-Eddine Hamri
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  3. Junwei Wang
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Correspondence to Mohammed-Salah Abdelouahab.

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Abdelouahab, MS., Hamri, NE. & Wang, J. Hopf bifurcation and chaos in fractional-order modified hybrid optical system. Nonlinear Dyn 69, 275–284 (2012). https://doi.org/10.1007/s11071-011-0263-4

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