A Chaotic Jerk System with Three Cubic Nonlinearities, Dynamical Analysis, Adaptive Chaos Synchronization and Circuit Simulation S Vaidyanathan1,*, A Sambas2 , S Zhang3 , Mujiarto2 , M Mamat4 and Subiyanto5
1Research and Development Centre, Vel Tech University, Avadi, Chennai, India
2Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia
3School of Physics and Opotoelectric Engineering, Xiangtan University, Hunan, China
4Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kuala
Terengganu, Malaysia
5Department of Marine Science, Faculty of Fishery and Marine Science, Universitas Padjadjaran, Indonesia
Abstract
A 3-D new chaotic jerk system with three cubic nonlinearities is proposed in this
paper. The dynamical properties of the new jerk system are described in terms of phase
portraits, Lyapunov exponents, Kaplan-Yorke dimension, symmetry, dissipativity, etc. Also, a
detailed dynamical analysis of the jerk system has been carried out with bifurcation diagram
and Lyapunov exponents. As an engineering application, adaptive synchronization of the new
chaotic jerk system with itself is designed via backstepping control method. Furthermore, an
electronic circuit realization of the new chaotic jerk system is presented in detail to confirm the
feasibility of the theoretical chaotic jerk model.
Keywords: Chaotic Jerk System, three Cubic, Nonlinearities
