A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control
In this research work, we propose a new four-dimensional chaotic hyperjerk system with four quadratic nonlinearities. We carry out a detailed bifurcation analysis and derive conditions for the existence of a Hopf bifurcation for the new hyperjerk system. A linear analysis shows that there is only a...
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| Language: | English |
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Polish Academy of Sciences
2024-12-01
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| Series: | Archives of Control Sciences |
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| Online Access: | https://journals.pan.pl/Content/133803/art02.pdf |
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| author | Sundarapandian Vaidyanathan Aceng Sambas Irene M. Moroz Chittineni Aruna Mohamad Afendee Mohamed Arun Sundaram |
| author_facet | Sundarapandian Vaidyanathan Aceng Sambas Irene M. Moroz Chittineni Aruna Mohamad Afendee Mohamed Arun Sundaram |
| author_sort | Sundarapandian Vaidyanathan |
| collection | DOAJ |
| description | In this research work, we propose a new four-dimensional chaotic hyperjerk system with four quadratic nonlinearities. We carry out a detailed bifurcation analysis and derive conditions for the existence of a Hopf bifurcation for the new hyperjerk system. A linear analysis shows that there is only a unique trivial equilibrium state, whose stability depends solely on the parameter p. The only bifurcation possible is a Hopf bifurcation when p = 2. This is verified from bifurcation transition diagrams.We derive new results showing multistability and the existence of coexisting attractors for the new chaotic hyperjerk system. Using MultiSim, a new electronic circuit is designed for the new chaotic hyperjerk system with four quadratic nonlinearities. Finally, we present a control application for the proposed chaotic hyperjerk system with four quadratic nonlinearities. Using active backstepping control, we design a new controller that achieves complete synchronization for the master-slave chaotic hyperjerk systems with four quadratic nonlinearities. |
| format | Article |
| id | doaj-art-d6f5dd2579e049c78da7b636df1d1ce2 |
| institution | Kabale University |
| issn | 1230-2384 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj-art-d6f5dd2579e049c78da7b636df1d1ce22024-12-31T08:47:27ZengPolish Academy of SciencesArchives of Control Sciences1230-23842024-12-01vol. 34No 4https://doi.org/10.24425/acs.2024.153098A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping controlSundarapandian Vaidyanathan0https://orcid.org/0000-0003-4696-908XAceng Sambas1https://orcid.org/0000-0002-1623-0770Irene M. Moroz2https://orcid.org/0000-0003-1503-939XChittineni Aruna3https://orcid.org/0009-0005-4427-1093Mohamad Afendee Mohamed4https://orcid.org/0000-0001-5985-3970Arun Sundaram5https://orcid.org/0000-0002-8915-3497Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062, Tamil Nadu, IndiaFaculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, 21300, Terengganu, MalaysiaMathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UKDepartment of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Vinjanampadu, Vatticherukuru Mandal, Guntur-522017, Andhra Pradesh, IndiaFaculty of Information and Computing, Universiti Sultan Zainal Abidin, Terengganu, MalaysiaDepartment of Electronics and Communication Engineering, Jerusalem College of Engineering, Narayanapuram, Pallikaranai, Chennai – 600 100, Tamil Nadu, IndiaIn this research work, we propose a new four-dimensional chaotic hyperjerk system with four quadratic nonlinearities. We carry out a detailed bifurcation analysis and derive conditions for the existence of a Hopf bifurcation for the new hyperjerk system. A linear analysis shows that there is only a unique trivial equilibrium state, whose stability depends solely on the parameter p. The only bifurcation possible is a Hopf bifurcation when p = 2. This is verified from bifurcation transition diagrams.We derive new results showing multistability and the existence of coexisting attractors for the new chaotic hyperjerk system. Using MultiSim, a new electronic circuit is designed for the new chaotic hyperjerk system with four quadratic nonlinearities. Finally, we present a control application for the proposed chaotic hyperjerk system with four quadratic nonlinearities. Using active backstepping control, we design a new controller that achieves complete synchronization for the master-slave chaotic hyperjerk systems with four quadratic nonlinearities.https://journals.pan.pl/Content/133803/art02.pdfchaotic systemschaoshyperjerk systemsbifurcation analysiscircuit designbackstepping controlsynchronization |
| spellingShingle | Sundarapandian Vaidyanathan Aceng Sambas Irene M. Moroz Chittineni Aruna Mohamad Afendee Mohamed Arun Sundaram A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control Archives of Control Sciences chaotic systems chaos hyperjerk systems bifurcation analysis circuit design backstepping control synchronization |
| title | A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control |
| title_full | A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control |
| title_fullStr | A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control |
| title_full_unstemmed | A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control |
| title_short | A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control |
| title_sort | new chaotic hyperjerk system with four quadratic nonlinearities its bifurcation analysis multistability circuit design and complete synchronization design via active backstepping control |
| topic | chaotic systems chaos hyperjerk systems bifurcation analysis circuit design backstepping control synchronization |
| url | https://journals.pan.pl/Content/133803/art02.pdf |
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