A Novel 3-D Conservative Jerk Chaotic System with Two Quadratic Nonlinearities and Its Adaptive Control

Abstract

In this research work, we announce a six-term novel 3-D conservative jerk chaotic system with two quadratic nonlinearities. The novel conservative jerk chaotic system is obtained by adding a quadratic nonlinearity to Sprott’s 3-D conservative jerk chaotic system (1997). In this work, we first discuss the qualitative properties of the novel 3-D conservative jerk chaotic system. Conservative chaotic systems are characterized by the property that they are volume conserving. The novel conservative jerk chaotic system has two saddle-foci equilibrium points. Thus, both equilibrium points of the novel conservative jerk chaotic system are unstable. We obtain the Lyapunov exponents of the novel conservative jerk chaotic system as \(L_1 = 0.0452\), \(L_2 = 0\) and \(L_3 = -0.0452\). Also, the Kaplan-Yorke dimension of the conservative novel jerk chaotic system is obtained as \(D_{KY} = 3\). The high value of the Kaplan-Yorke dimension indicates the complexity of the novel conservative jerk chaotic system. Next, an adaptive backstepping controller is designed to stabilize the novel conservative jerk chaotic system with unknown system parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel conservative jerk chaotic systems with unknown system parameters. The main control results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the main results on the novel 3-D conservative jerk chaotic system.