Adaptive Backstepping Control, Synchronization and Circuit Simulation of a Novel Jerk Chaotic System with a Quartic Nonlinearity

Abstract

This work describes a six-term novel 3-D jerk chaotic system with a quartic nonlinearity. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the novel jerk system are discussed. The novel jerk chaotic system has exactly one equilibrium point, which is saddle-focus. The Lyapunov exponents of the novel jerk chaotic system are obtained as \(L_1 = 0.1443, L_2 = 0\) and \(L_3 = -2.8439\). The Kaplan–Yorke dimension of the novel jerk chaotic system is obtained as \(D_{KY} = 2.0507\). Next, an adaptive backstepping controller is designed to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been shown to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.