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.

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

“…To eliminate this problem, an observer design scheme was used to determine the unavailable states of the system. Consequently, the observer design has garnered considerable attention from researchers in the past few decades owing to its importance in fault diagnosis, energy system analysis, chaos-based secure communications, and synchronization studies [5], [6], [7], [8]. When designing an observer, the stability of the system must be ensured under output delays and resistance to external disturbances.…”

“…Figures 4,5,and 6 show the plots of the states and estimation errors for the proposed robust observer-based control in the presence of perturbations. The estimation error converges in the neighborhood or origin, even in the presence of a disturbance.…”

Design of a New Chaotic System with Sine Function: Dynamic Analysis and Offset Boosting Control

“…Sahoo and Roy (2022) In the past few decades, the chaos synchronization has great attention since it can be used to solve many issues in secure communication system. Recently, various adaptive synchronization scheme Rahman and Jasim (2022) This motivates me in this study to construct another trigonometry function based chaotic system. The proposed system presents offset boosting control property which means the position of the attractor can be easily controlled by adding a controller with any one of the state signals of the system.…”

Effect of Support Stiffness Nonlinearity on the Low-Frequency Vibro-Acoustic Characteristics for a Mechanical Equipment—Floating Raft—Underwater Cylindrical Shell Coupled System

“…Yan et al [19] proposed a novel bi-state nonlinear vibration isolator, whose motion can be either periodic or chaotic. Rahman et al [20] proposed a new fractional-order chaotic system containing multiple nonlinear terms, which can excite hidden chaotic attractors or self-excited chaotic attractors depending on the chosen system parameters or the value of its fractional-order derivative. Li et al [21] proposed an SRN feature extraction method combining maximum relevance minimum redundancy, which can effectively classify different chaotic signals.…”