Title: Modelling, bifurcation analysis, circuit design and FPGA-based implementation of a new chaotic jerk system exhibiting Hopf bifurcations

Authors: Sundarapandian Vaidyanathan; Irene M. Moroz; Aceng Sambas; Daniel Clemente-Lopez; Jesus Manuel Munoz-Pacheco; Jose de Jesus Rangel-Magdaleno

Addresses: Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062, Tamil Nadu, India ' Mathematical Institute, University of Oxford, Oxford OX2 6GG, England, UK ' 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 ' Digital Systems Group, Department of Electronics, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintila, Puebla 72840, Mexico ' Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, 4 Sur 104, Colonia Centro, C.P. 72000, Puebla, Mexico ' Digital Systems Group, Department of Electronics, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Tonantzintila, Puebla 72840, Mexico

Abstract: It is well-known that chaotic systems have several applications in scientific modelling and engineering fields such as encryption, cryptosystems, secure communication, etc. This work proposes a three-dimensional mechanical chaotic system with jerk dynamics. A detailed bifurcation analysis is conducted for the proposed chaotic system. It is shown that the proposed chaotic system has two equilibrium points which exhibit Hopf bifurcations. It is also shown that the proposed chaotic system depicts multi-stability and co-existing chaotic attractors. Using MultiSim (Version 14), an electronic circuit is designed for the proposed mechanical chaotic system with jerk dynamics. As another engineering application, field programmable gate array (FPGA) design has been made for the proposed mechanical jerk chaotic system. Euler's finite-difference method is used for our FPGA design. A hardware implementation of the FPGA-based design is performed in this work and experimental results are given in detail.

Keywords: mechanical systems; jerk systems; chaos; chaotic systems; multi-stability; Hopf bifurcations; MultiSim design; circuit design; FPGA implementation; Euler's method.

DOI: 10.1504/IJMIC.2024.136637

International Journal of Modelling, Identification and Control, 2024 Vol.44 No.2, pp.107 - 120

Received: 02 Nov 2022
Accepted: 05 Jan 2023
Published online: 09 Feb 2024 *

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