A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control

• Autorzy: Vaidyanathan Sundarapandian , Sambas Aceng , Moroz Irene M. , Aruna Chittineni , Mohamed Mohamad Afendee , Sundaram Arun

Identyfikatory

DOI

10.24425/acs.2024.153098

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

chaotic systems; chaos; hyperjerk systems; bifurcation analysis; circuit design; backstepping control; synchronization

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 4
• Strony: 697--713
• Opis fizyczny: Bibliogr. 20 poz., rys., wzory

Twórcy

autor

Vaidyanathan Sundarapandian

• Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062, Tamil Nadu, India
• Faculty of Information and Computing, Universiti Sultan Zainal Abidin, Terengganu, Malaysia

• https://orcid.org/0000-0003-4696-908X

autor

Sambas Aceng

• Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, 21300, Terengganu, Malaysia
• Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Jawa Barat 46196, Indonesia

• https://orcid.org/0000-0002-1623-0770

autor

Moroz Irene M.

• Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UK

• https://orcid.org/0000-0003-1503-939X

autor

Aruna Chittineni

• Department of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Vinjanampadu, Vatticherukuru Mandal, Guntur-522017, Andhra Pradesh, India

• https://orcid.org/0009-0005-4427-1093

autor

Mohamed Mohamad Afendee

• Faculty of Information and Computing, Universiti Sultan Zainal Abidin, Terengganu, Malaysia

• https://orcid.org/0000-0001-5985-3970

autor

Sundaram Arun

• Department of Electronics and Communication Engineering, Jerusalem College of Engineering, Narayanapuram, Pallikaranai, Chennai - 600 100, Tamil Nadu, India

• https://orcid.org/0000-0002-8915-3497

Bibliografia

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