Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization
Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in eac...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/781594 |
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| _version_ | 1832545856584155136 |
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| author | Jiezhi Wang Qing Zhang Zengqiang Chen Hang Li |
| author_facet | Jiezhi Wang Qing Zhang Zengqiang Chen Hang Li |
| author_sort | Jiezhi Wang |
| collection | DOAJ |
| description | Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme. |
| format | Article |
| id | doaj-art-66458ae4c8ec41ebac14453e53c5904e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-66458ae4c8ec41ebac14453e53c5904e2025-02-03T07:24:29ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/781594781594Ultimate Bound of a 3D Chaotic System and Its Application in Chaos SynchronizationJiezhi Wang0Qing Zhang1Zengqiang Chen2Hang Li3College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaEconomics and Management College, Civil Aviation University of China, Tianjin 300300, ChinaTwo ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme.http://dx.doi.org/10.1155/2014/781594 |
| spellingShingle | Jiezhi Wang Qing Zhang Zengqiang Chen Hang Li Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization Abstract and Applied Analysis |
| title | Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization |
| title_full | Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization |
| title_fullStr | Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization |
| title_full_unstemmed | Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization |
| title_short | Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization |
| title_sort | ultimate bound of a 3d chaotic system and its application in chaos synchronization |
| url | http://dx.doi.org/10.1155/2014/781594 |
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