A Novel Conservative Jerk Chaotic System With Two Cubic Nonlinearities and Its Adaptive Backstepping Control

Abstract

First, this work announces a six-term novel 3-D conservative jerk chaotic system with two cubic nonlinearities. The conservative chaotic systems are characterized by the property that they are volume conserving. The phase portraits of the novel conservative jerk chaotic system are displayed and the qualitative properties of the novel system are discussed. The novel jerk chaotic system has three unstable equilibrium points. The Lyapunov exponents of the novel jerk chaotic system are obtained as \(L_1 = 0.01562, L_2 = 0\) and \(L_3 = -0.01562\). The Kaplan–Yorke dimension of the novel jerk chaotic system is obtained as \(D_{KY} = 3\). Next, an adaptive backstepping controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical conservative 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 conservative jerk chaotic system and also the adaptive backstepping control results.