Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium

Sundarapandian Vaidyanathan, Ahmad Taher Azar (), Ibrahim A. Hameed (), Khaled Benkouider, Esteban Tlelo-Cuautle, Brisbane Ovilla-Martinez, Chang-Hua Lien and Aceng Sambas
Additional contact information
Sundarapandian Vaidyanathan: Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai 600 062, Tamil Nadu, India
Ahmad Taher Azar: College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Ibrahim A. Hameed: Department of ICT and Natural Sciences, Norwegian University of Science and Technology, Larsgardsvegen, 2, 6009 Alesund, Norway
Khaled Benkouider: Non Destructive Testing Laboratory, Automatic Department, Jijel University, BP 98, Jijel 18000, Algeria
Esteban Tlelo-Cuautle: Electronics Department, Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Puebla 72840, Mexico
Brisbane Ovilla-Martinez: Computer Science Department, CINVESTAV—The Center for Research and Advanced Studies of the National Polytechnic Institute, Av. IPN 2508, Mexico City 07360, Mexico
Chang-Hua Lien: Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 81157, Taiwan
Aceng Sambas: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak 21300, Terengganu, Malaysia

Mathematics, 2023, vol. 11, issue 12, 1-22

Abstract: This research paper addresses the modelling of a new 3-D chaotic jerk system with a stable equilibrium. Such chaotic systems are known to exhibit hidden attractors. After the modelling of the new jerk system, a detailed bifurcation analysis has been performed for the new chaotic jerk system with a stable equilibrium. It is shown that the new jerk system has multistability with coexisting attractors. Next, we apply backstepping control for the synchronization design of a pair of new jerk systems with a stable equilibrium taken as the master-slave chaotic systems. Lyapunov stability theory is used to establish the synchronization results for the new jerk system with a stable equilibrium. Finally, we show that the FPGA design of the new jerk system with a stable equilibrium can be implemented using the FPGA Zybo Z7-20 development board. The design of the new jerk system consists of multipliers, adders and subtractors. It is observed that the experimental attractors are in good agreement with simulation results.

Keywords: jerk systems; chaos; hidden attractors; bifurcation analysis; multistability; FPGA design; backstepping control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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