Title: A new multistable hyperjerk dynamical system with self-excited chaotic attractor, its complete synchronisation via backstepping control, circuit simulation and FPGA implementation

Authors: Sundarapandian Vaidyanathan; Esteban Tlelo-Cuautle; Aceng Sambas; Leutcho Gervais Dolvis; Omar Guillén-Fernández; Babatunde A. Idowu

Addresses: Research and Development Centre, Vel Tech University, Chennai-600062, Tamil Nadu, India ' Department of Electronics, INAOE, Tonantzintla, Puebla 72840, Mexico ' Department of Mechanical Engineering, Universitas Muhammadiyah Taskimalaya, Tasikmalaya, Jawa Barat 46196, Indonesia ' Laboratory of Condensed Matter, Electronics and Signal Processing, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon ' Department of Electronics, INAOE, Tonantzintla, Puebla 72840, Mexico ' Department of Physics, Lagos State University, Ojo, 102101, Lagos, Nigeria

Abstract: In this work, we report a new 4D chaotic hyperjerk system and present a detailed dynamic analysis of the new system with Lyapunov exponents, bifurcation plots, etc. We find that the new hyperjerk system exhibits multistability and coexisting chaotic attractors. The hyperjerk system has a unique saddle-focus rest point at the origin, which is unstable. This shows that the new chaos hyperjerk system has a self-excited chaotic attractor. As an application of backstepping control, we obtain new results for the global chaos complete synchronisation of pair of chaotic hyperjerk systems. A circuit model using MultiSim of the new chaotic hyperjerk system is designed for applications in practice. Finally, an FPGA-based implementation of the new chaotic hyperjerk dynamical system is performed by applying two numerical methods and their corresponding hardware resources are given.

Keywords: chaos; chaotic systems; hyperjerk; backstepping control; synchronisation; circuit design; FPGA design.

DOI: 10.1504/IJMIC.2020.114192

International Journal of Modelling, Identification and Control, 2020 Vol.35 No.3, pp.177 - 190

Received: 17 Apr 2020
Accepted: 05 Jun 2020

Published online: 08 Apr 2021 *

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