Hidden Dynamics Investigation, Fast Adaptive Synchronization, and Chaos-Based Secure Communication Scheme of a New 3D Fractional-Order Chaotic System

Abstract

In this paper, a new fractional-order chaotic system containing several nonlinearity terms is introduced. This new system can excite hidden chaotic attractors or self-excited chaotic attractors depending on the chosen system parameters or its fraction-order derivative value. Several dynamics of this new system, such as chaotic attractors, equilibrium points, Lyapunov exponents, and bifurcation diagrams, are analyzed analytically and numerically. Then, adaptive control laws are developed to achieve chaos synchronization in two identical new systems with uncertain parameters; one of these two new identical systems is the master, and the other is the slave. In addition, update laws for estimating the uncertain slave parameters are derived. Furthermore, in chaos application fields, these master and slave synchronized systems are applied in secure communication to act as the transmitter and receiver, respectively. Finally, the security analysis metric tests were analyzed using histograms and spectrograms to establish the communication system’s security strength. Numerical test results demonstrate the possibility of using this proposed fractional-order chaotic system in high-security communication systems. The employed communication system is also highly resistant to pirate attacks.