Dynamic Analysis for a Fractional-Order Autonomous Chaotic System

Dynamic Analysis for a Fractional-Order Autonomous Chaotic System

We introduce a discretization process to discretize a modified fractional-order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient...

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Main Authors: Jiangang Zhang, Juan Nan, Wenju Du, Yandong Chu, Hongwei Luo
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/8712496
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spelling doaj-46621917acf345a4a96f9cf9d35b60772020-11-24T22:25:53ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/87124968712496Dynamic Analysis for a Fractional-Order Autonomous Chaotic SystemJiangang Zhang0Juan Nan1Wenju Du2Yandong Chu3Hongwei Luo4School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaWe introduce a discretization process to discretize a modified fractional-order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient conditions of stability of the discrete system are investigated. The results show that the system’s fractional parameter has an effect on the stability of the discrete system, and the system has rich dynamic characteristics such as Hopf bifurcation, attractor crisis, and chaotic attractors.http://dx.doi.org/10.1155/2016/8712496
collection DOAJ
language English
format Article
sources DOAJ
author Jiangang Zhang
Juan Nan
Wenju Du
Yandong Chu
Hongwei Luo
spellingShingle Jiangang Zhang
Juan Nan
Wenju Du
Yandong Chu
Hongwei Luo
Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
Discrete Dynamics in Nature and Society
author_facet Jiangang Zhang
Juan Nan
Wenju Du
Yandong Chu
Hongwei Luo
author_sort Jiangang Zhang
title Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
title_short Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
title_full Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
title_fullStr Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
title_full_unstemmed Dynamic Analysis for a Fractional-Order Autonomous Chaotic System
title_sort dynamic analysis for a fractional-order autonomous chaotic system
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2016-01-01
description We introduce a discretization process to discretize a modified fractional-order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient conditions of stability of the discrete system are investigated. The results show that the system’s fractional parameter has an effect on the stability of the discrete system, and the system has rich dynamic characteristics such as Hopf bifurcation, attractor crisis, and chaotic attractors.
url http://dx.doi.org/10.1155/2016/8712496
work_keys_str_mv AT jiangangzhang dynamicanalysisforafractionalorderautonomouschaoticsystem
AT juannan dynamicanalysisforafractionalorderautonomouschaoticsystem
AT wenjudu dynamicanalysisforafractionalorderautonomouschaoticsystem
AT yandongchu dynamicanalysisforafractionalorderautonomouschaoticsystem
AT hongweiluo dynamicanalysisforafractionalorderautonomouschaoticsystem
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