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

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

Chaos, Solitons & Fractals, 2017, vol. 99, issue C, 116-123

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.

Keywords: Fractional-order system; Feigenbaum's constants in reverse bifurcation; Rössler system (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:99:y:2017:i:c:p:116-123

DOI: 10.1016/j.chaos.2017.03.014

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