Journal of Engineering Science and Technology Review (Nov 2014)
A 3-D Novel Highly Chaotic System with Four Quadratic Nonlinearities, its Adaptive Control and Anti-Synchronization with Unknown Parameters
Abstract
This research work proposes a seven-term 3-D novel dissipative chaotic system with four quadratic nonlinearities. The Lyapunov exponents of the 3-D novel chaotic system are obtained as L1 = 11.36204, L2 = 0 and L3 = –47.80208. Since the sum of the Lyapunov exponents is negative, the 3-D novel chaotic system is dissipative. Also, the Kaplan-Yorke dimension of the 3-D novel chaotic system is obtained as DKY = 2.23769. The maximal Lyapunov exponent (MLE) of the novel chaotic system is L1 = 11.36204, which is a large value for a polynomial chaotic system. Thus, the proposed 3-D novel chaotic system is highly chaotic. The phase portraits of the novel chaotic system simulated using MATLAB depict the highly chaotic attractor of the novel system. This research work also discusses other qualitative properties of the system. Next, an adaptive controller is designed to stabilize the 3-D novel chaotic system with unknown parameters. Also, an adaptive synchronizer is designed to achieve anti-synchronization of the identical 3-D novel chaotic systems with unknown parameters. The adaptive results derived in this work are established using Lyapunov stability theory. MATLAB simulations have been shown to illustrate and validate all the main results derived in this work.
