Adaptive backstepping control and synchronization of a novel 3-D jerk system with an exponential nonlinearity

Abstract

In this research work, we announce a seven-term novel 3-D jerk chaotic system with an exponential nonlinearity. First, we discuss the qualitative properties of the novel jerk chaotic system. The novel jerk chaotic system has a unique equilibrium point, which is a saddle-focus. Thus, the unique equilibrium point is unstable. We obtain the Lyapunov exponents of the novel jerk chaotic system as L1 = 0.1066, L2 = 0 and L3 = −1.1047. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.0965. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with unknown system parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel 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 developed in this work.