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Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system

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  • Li, Zengshan
  • Chen, Diyi
  • Ma, Mengmeng
  • Zhang, Xinguang
  • Wu, Yonghong

Abstract

This paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcation is provided. Third, in order to observe the effect of fractional-order to Feigenbaum's constants in reverse bifurcation, a series of bifurcation diagrams are computed. The Feigenbaum's constants in reverse bifurcation are measured and the error percentage in fractional-order Rössler system is presented. The simulation results show that Feigenbaum's constants exist in reverse bifurcation for fractional-order Rössler system. Especially, the Feigenbaum's constants still exist in the periodic windows. A summary on previous others’ works about Feigenbaum's constants is proposed. This paper draw a conclusion that the constants are universal in both period-doubling bifurcation and reverse bifurcation for both integer and fractional-order system.

Suggested Citation

  • Li, Zengshan & Chen, Diyi & Ma, Mengmeng & Zhang, Xinguang & Wu, Yonghong, 2017. "Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 116-123.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:116-123
    DOI: 10.1016/j.chaos.2017.03.014
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    References listed on IDEAS

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