Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based-Free Mode

An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi stable fractional-order chaotic system. Firstly, some dynamical features of the system are described, and the chaotic behaviour of the system is verified. Then, both spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. Besides, the combination of a new chattering-free robust sliding mode controller with a neural network observer is proposed for the synchronization of the fractional-order system. With the neural network estimator, unknown functions of the system are obtained, and the effects of disturbances are completely taken into account. Also, based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. Lastly, the proposed control technique is applied to the fractional-order system. Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

A vast amount of research has been devoted to chaotic systems due to their diverse applications. This study investigates a multi-stable fractional-order chaotic system and proposes a new control method using a neural network for synchronization and disturbance rejection. The results demonstrate the effectiveness and disturbance rejection capability of the proposed method.