Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor-Reference-Cited by-同舟云学术

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

Published:2019-01-01 Issue: Volume:2019 Page:1-15
ISSN:1026-0226
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Liu Xiaojun¹²^ORCID,Hong Ling³^ORCID,Yang Lixin⁴^ORCID,Tang Dafeng³

Affiliation:

1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

2. School of Sciences, Xi’an University of Architecture and Technology, Xi’an 710055, China

3. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China

4. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2019/8341514.pdf

Reference32 articles.

1. Pseudochaotic Systems and Their Fractional Kinetics

2. A fractional calculus perspective of distributed propeller design

3. Fractional State Space Analysis of Economic Systems

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