Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities

Abstract

This research work introduces a six-term novel 3-D polynomial chaotic system with three quadratic nonlinearities. Phase portraits and detailed qualitative analysis of the polynomial novel chaotic system are described. Lyapunov exponents and Lyapunov dimension for the novel chaotic system have been obtained. The maximal Lyapunov exponent (MLE) for the novel polynomial chaotic system has been found to have a large value, viz. L1 = 10.2234. Thus, the novel 3-D chaotic system exhibits strong chaotic behaviour. New results are derived for the adaptive control and adaptive synchronisation of the novel 3-D polynomial chaotic system with unknown parameters using Lyapunov stability theory. MATLAB plots have been shown to illustrate the phase portraits of the novel 3-D chaotic system and the adaptive results derived in this paper.