Qualitative analysis of a novel 5D chaotic system based on Bouali’s system and its application in private communication via adaptive control

This research work offers a novel five-dimensional chaotic system based on the renowned Bouali system. The dynamics of this system is thoroughly investigated by estimating the Lyapunov exponents, displaying its phase portraits, bifurcation scenarios, Poincaré map, time-series and by identifying the Kaplan–Yorke dimension. The stagnation points are also determined and their detailed stability analysis is addressed. The technique of adaptive control is employed to achieve several synchronizations between identical systems. Based on theory of Lyapunov stability, appropriate controllers are designed to obtain these distinct synchronizations. All the theoretical results are confirmed for their accuracy and efficacy through numerical simulations on MATLAB.