Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control
Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise line...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/615187 |
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| author | Chunyan Han Fang Yuan Xiaoyuan Wang |
| author_facet | Chunyan Han Fang Yuan Xiaoyuan Wang |
| author_sort | Chunyan Han |
| collection | DOAJ |
| description | Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol. |
| format | Article |
| id | doaj-art-4e68c0e9aae24300ad43b6959a635f7c |
| institution | Kabale University |
| issn | 2314-4904 2314-4912 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Engineering |
| spelling | doaj-art-4e68c0e9aae24300ad43b6959a635f7c2025-02-03T05:46:33ZengWileyJournal of Engineering2314-49042314-49122015-01-01201510.1155/2015/615187615187Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching ControlChunyan Han0Fang Yuan1Xiaoyuan Wang2School of Automation, Guangdong University of Technology, Guangzhou 510006, ChinaSchool of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Electronics and Information, Hangzhou Dianzi University, Hangzhou 310018, ChinaBased on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.http://dx.doi.org/10.1155/2015/615187 |
| spellingShingle | Chunyan Han Fang Yuan Xiaoyuan Wang Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control Journal of Engineering |
| title | Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control |
| title_full | Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control |
| title_fullStr | Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control |
| title_full_unstemmed | Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control |
| title_short | Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control |
| title_sort | generation method of multipiecewise linear chaotic systems based on the heteroclinic shil nikov theorem and switching control |
| url | http://dx.doi.org/10.1155/2015/615187 |
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