A novel four-dimensional conservative chaotic system without linear term, its analysis and adaptive control via integral sliding mode control

Abstract

In this work, a novel conservative four-dimensional chaotic system without linear term is proposed. The fundamental qualitative properties of the novel chaotic system are described with details of volume preserving property, equilibrium points, symmetry, Lyapunov exponents and Kaplan-Yorke dimension. We show that the novel four-dimensional chaotic system has two planes and one line of equilibrium points. Next, an adaptive integral sliding mode controller is designed to stabilise the novel chaotic system with an unknown system parameter. Moreover, an adaptive integral sliding mode controller is designed to achieve global chaos synchronisation of the identical novel chaotic systems with an unknown system parameter. The adaptive control mechanism helps the control design by estimating the unknown parameter. Numerical simulations using MATLAB are shown to illustrate all the main results derived in this work.