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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/8712496 |
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| _version_ | 1849407124751253504 |
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| author | Jiangang Zhang Juan Nan Wenju Du Yandong Chu Hongwei Luo |
| author_facet | Jiangang Zhang Juan Nan Wenju Du Yandong Chu Hongwei Luo |
| author_sort | Jiangang Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-46621917acf345a4a96f9cf9d35b6077 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-46621917acf345a4a96f9cf9d35b60772025-08-20T03:36:11ZengWileyDiscrete 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 |
| 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 |
| title | 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_short | Dynamic Analysis for a Fractional-Order Autonomous Chaotic System |
| title_sort | dynamic analysis for a fractional order autonomous chaotic system |
| 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 |