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,
Aceng Sambas
Affiliations
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
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.
