Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor - Xiaojun Liu; Ling Hong; Lixin Yang; Dafeng Tang (Discrete Dynamics in Nature and Society)
In this paper, a new fractional-order system which has a chaotic attractor of the one-scroll structure is presented. Firstly, the stability of the equilibrium points of the system is investigated. And based on the stability analysis, the generation conditions of the one-scroll structure for the attractor are determined. In a commensurate-order case, bifurcations with the variation of a system parameter are investigated as derivative orders decrease from 0.99. In an incommensurate-order case, bifurcations with the variation of a derivative order are analyzed as other orders decrease from 1.