Analysis, Control, Synchronization and LabVIEW Implementation of a Seven- Term Novel Chaotic System

First, this paper announces a seven-term novel 3-D chaotic system with a cubic nonlinearity and two quadratic nonlinearities. The phase portraits of the novel 3-D chaotic system are displayed and the mathematical properties are discussed. The proposed novel 3-D chaotic system has three equilibrium points, which are all unstable. We shall show that the equilibrium point at the origin is a saddle point, while the other two equilibrium points are saddle-foci. The Lyapunov exponents of the novel 3-D chaotic system are obtained as L 1 = 3.20885, L 2 = 0 and L 3 = –23.63597. Thus, the Maximal Lyapunov Exponent (MLE) of the novel 3-D chaotic system is obtained as L 1 = 3.20885. Also, the Kaplan-Yorke dimension of the novel 3-D chaotic system is derived as D KY = 2.13576. Since the sum of the Lyapunov exponents of the novel chaotic system is negative, it follows that the novel chaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel 3-D chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global and exponential synchronization of the identical novel 3-D chaotic systems with unknown parameters. The main adaptive results for stabilization and synchronization are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this work. Finally, a circuit design of the novel 3-D chaotic system is implemented in LabVIEW to validate the theoretical chaotic model.