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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/8341514 |
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| _version_ | 1832548203285708800 |
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| author | Xiaojun Liu Ling Hong Lixin Yang Dafeng Tang |
| author_facet | Xiaojun Liu Ling Hong Lixin Yang Dafeng Tang |
| author_sort | Xiaojun Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8d1b3215b51347368ed6236c757a36d9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8d1b3215b51347368ed6236c757a36d92025-02-03T06:42:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/83415148341514Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic AttractorXiaojun Liu0Ling Hong1Lixin Yang2Dafeng Tang3School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaState Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, ChinaState Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, ChinaIn 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.http://dx.doi.org/10.1155/2019/8341514 |
| spellingShingle | Xiaojun Liu Ling Hong Lixin Yang Dafeng Tang Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor Discrete Dynamics in Nature and Society |
| title | Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor |
| title_full | Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor |
| title_fullStr | Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor |
| title_full_unstemmed | Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor |
| title_short | Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor |
| title_sort | bifurcations of a new fractional order system with a one scroll chaotic attractor |
| url | http://dx.doi.org/10.1155/2019/8341514 |
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