Open AccessBifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor
Author(s) -
Xiaojun Liu,
Hong Liu,
Lixin Yang,
Dafeng Tang
Publication year - 2019
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2019/8341514
Subject(s) - attractor , scroll , chaotic , mathematics , stability (learning theory) , order (exchange) , derivative (finance) , fractional order system , bifurcation , control theory (sociology) , poincaré map , fractional calculus , mathematical analysis , computer science , nonlinear system , physics , control (management) , archaeology , finance , quantum mechanics , artificial intelligence , machine learning , financial economics , economics , history
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.