Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system
MetadataShow full item record
© 2017 Elsevier LtdThis 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.
Showing items related by title, author, creator and subject.
Wang, F.; Chen, Diyi; Zhang, Xinguang; Wu, Yong Hong (2017)© 2016 Informa UK Limited, trading as Taylor & Francis Group.This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace ...
Improvement of the Control System Performance based on Fractional-Order PID Controllers and Models with Robustness ConsiderationsMeneses, H.; Guevara, E.; Arrieta, O.; Padula, Fabrizio; Vilanova, R.; Visioli, A. (2018)© 2018 In this paper we assess the performance improvement achievable by using onedegree-of-freedom fractional-order proportional-integral-derivative controllers (FOPI/FOPID) instead of their integer-order counterparts ...
Padula, Fabrizio; Visioli, A. (2015)This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems ...