Dynamical Features and Complete Synchronization of Unified Chaotic Systems With Caputo-Hadamard Fractional Derivative

Abstract

This paper investigates the dynamical characteristics and synchronization of a unified chaotic system described by Caputo–Hadamard fractional derivative. The equilibrium solutions of the considered system are first analyzed and confirmed to be unstable. Then, by observing the phase diagram and calculating the largest Lyapunov exponent, we discuss the dynamical behavior of the fractional unified chaotic system in relation to variations in both inherent parameters and fractional order. The result indicates that the dynamic states of the system are influenced by these two parameters. The chaos synchronization of fractional unified chaotic systems is explored using a drive-response synchronization method, wherein two controllers are designed to achieve complete synchronization between the driving and responding systems. Furthermore, this proposed chaos synchronization approach for the fractional unified chaotic system is successfully applied to secure communication. Finally, numerical simulations illustrate how both inherent parameters of the system and fractional order affect synchronization performance.