Title: A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation

Authors: Sundarapandian Vaidyanathan; Irene M. Moroz; Aceng Sambas

Addresses: Research and Development Centre, Vel Tech University, Chennai, 600062, Tamil Nadu, India ' Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UK ' Department of Mechanical Engineering, Universitas Muhammadiyah Taskimalaya, Tasikmalaya, Jawa Barat 46196, Indonesia

Abstract: A new 4D dynamical hyperjerk system with hyperchaos is reported in this work. The proposed nonlinear mechanical system with hyperchaos has two saddle-focus rest points exhibiting Hopf bifurcations. A detailed bifurcation analysis of the new hyperjerk plant with theory and simulations is discussed. As a control application, an integral sliding mode controller has been designed for the global hyperchaos synchronisation of the new hyperjerk system with itself. Finally, a circuit model using MultiSim of the new hyperjerk system with hyperchaos is designed for practical implementation.

Keywords: hyperchaos; hyperchaotic systems; hyperjerk; bifurcations; sliding mode control; synchronisation; circuit design.

DOI: 10.1504/IJMIC.2019.107481

International Journal of Modelling, Identification and Control, 2019 Vol.33 No.4, pp.299 - 310

Received: 17 Sep 2019
Accepted: 14 Oct 2019
Published online: 29 May 2020 *

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