Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5499664 | Chaos, Solitons & Fractals | 2017 | 8 Pages |
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Li Zengshan, Chen Diyi, Ma Mengmeng, Zhang Xinguang, Wu Yonghong,