Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities
In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2014-09-01
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| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/acsc.2014.24.issue-3/acsc-2014-0022/acsc-2014-0022.xml?format=INT |
| _version_ | 1818148311533617152 |
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| author | Vaidyanathan Sundarapandian Volos Christos Pham Viet-Thanh Madhavan Kavitha Idowu Babatunde A. |
| author_facet | Vaidyanathan Sundarapandian Volos Christos Pham Viet-Thanh Madhavan Kavitha Idowu Babatunde A. |
| author_sort | Vaidyanathan Sundarapandian |
| collection | DOAJ |
| description | In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model |
| first_indexed | 2024-12-11T12:49:08Z |
| format | Article |
| id | doaj.art-6ffceab67cee431b8f7b3a49478bf0de |
| institution | Directory Open Access Journal |
| issn | 2300-2611 |
| language | English |
| last_indexed | 2024-12-11T12:49:08Z |
| publishDate | 2014-09-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-6ffceab67cee431b8f7b3a49478bf0de2022-12-22T01:06:45ZengPolish Academy of SciencesArchives of Control Sciences2300-26112014-09-0124337540310.2478/acsc-2014-0022acsc-2014-0022Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearitiesVaidyanathan Sundarapandian0Volos Christos1Pham Viet-Thanh2Madhavan Kavitha3Idowu Babatunde A.4Research and Development Centre, Vel Tech University, Avadi, Chennai- 600062, Tamilnadu, IndiaPhysics Department, Aristotle University of Thessaloniki, GR-54124, GreeceSchool of Electronics and Telecommunications, Hanoi University of Science and Technology 01 Dai Co Viet, Hanoi, VietnamDepartment of Mathematics, Vel Tech University, Avadi, Chennai- 600062, Tamilnadu, IndiaDepartment of Physics, Lagos State University, Ojo, Lagos, NigeriaIn this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical modelhttp://www.degruyter.com/view/j/acsc.2014.24.issue-3/acsc-2014-0022/acsc-2014-0022.xml?format=INTchaosjerk systemnovel systemadaptive controlbackstepping controlchaos synchronization |
| spellingShingle | Vaidyanathan Sundarapandian Volos Christos Pham Viet-Thanh Madhavan Kavitha Idowu Babatunde A. Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities Archives of Control Sciences chaos jerk system novel system adaptive control backstepping control chaos synchronization |
| title | Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| title_full | Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| title_fullStr | Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| title_full_unstemmed | Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| title_short | Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| title_sort | adaptive backstepping control synchronization and circuit simulation of a 3 d novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities |
| topic | chaos jerk system novel system adaptive control backstepping control chaos synchronization |
| url | http://www.degruyter.com/view/j/acsc.2014.24.issue-3/acsc-2014-0022/acsc-2014-0022.xml?format=INT |
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