Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor

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 attr...

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2019, Vol.2019 (2019), p.1-15
Main Authors: Tang, Dafeng, Yang, Li-xin, Hong, Ling, Liu, Xiaojun
Format: Article
Language:English
Subjects:
Bifurcations
Calculus
Chaos theory
Communication
Investigations
Kalman filters
Ordinary differential equations
Science
Stability analysis
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2019/8341514