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

Abstract

This research work describes a nine-term 3-D novel chaotic system with four quadratic nonlinearities. First, this work describes the dynamic analysis of the novel chaotic system and qualitative properties of the novel chaotic system are derived. The Lyapunov exponents of the nine-term novel chaotic system are obtained as $$ L_{1} = 9.45456,\;L_{2} = 0 $$ and $$ L_{3} = - 30.50532 $$ . Since the maximal Lyapunov exponent (MLE) of the novel chaotic system is $$ L_{1} = 9.45456 $$ , which is a high value, the novel chaotic system exhibits strong chaotic properties. Next, this work describes the adaptive control of the novel chaotic system with unknown system parameters. Also, this work describes the adaptive synchronization of the identical novel chaotic systems with unknown system parameters. The adaptive control and synchronization results are proved using Lyapunov stability theory. MATLAB simulations are given to demonstrate and validate all the main results derived in this work for the nine-term 3-D novel chaotic system.