Chaotic Analysis and Improved Finite-Time Adaptive Stabilization of a Novel 4-D Hyperchaotic System

Abstract

Chaotic systems are evidently very sensitive to slight perturbations in their algebraic structures and initial conditions, which can result in unpredictability of their future states. This characteristic has rendered them very useful in modelling and design of engineering and non-engineering systems. Using the Burke-Shaw chaotic system as a reference template, a special case of a novel 4-D hyperchaotic system is proposed. The system consists of 10 terms and 9 bounded parameters.  In this paper, after the realization of a mathematical model of the novel system, we designed an autonomous electronic circuit equivalent of the model and subsequently proposed an improved adaptive finite-time stabilizing controllers which incorporates some augmented strength coefficients in the derived controller structures. These augmented coefficients greatly constrained transient overshoots and resulted in a faster convergence time for the controlled trajectories of the novel system. This novel system is suitable for application in the modelling and design of information security systems such as image encryption and multimedia security systems, due to its good bifurcation property.