Analysis, Adaptive Control and Synchronization of a Seven-Term Novel 3-D Chaotic System

First, this paper introduces a seven-term novel 3-D chaotic system and discusses its qualitative properties. The proposed system is a seven-term novel polynomial chaotic system with three quadratic nonlinearities. The Lyapunov exponents of the novel chaotic system are obtained as L1 = 3.3226, L2 = 0 and L3 = –30.3406. The maximal Lyapunov exponent (MLE) for the novel chaotic system is obtained as L1 = 3.3226 and Lyapunov dimension as DL = 2.1095. Next, we derive new results for the adaptive control design of the novel chaotic system with unknown parameters. Next, we derive new results for the adaptive synchronization design of the identical novel chaotic systems with unknown parameters. The adaptive control and synchronization results have been established using adaptive control theory and Lyapunov stability theory. Numerical simulations with MATLAB have been shown to validate and illustrate all the new results derived in this paper.