A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Abstract

This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

“…, 4) represent constant gains. The improved dynamic surface (24) speeds up the dynamic response with a fast decay rate. The initial condition of ( 25) and ( 26) is considered to be…”

“…In this method, the slave system modes must be adjusted with a control approach so that they eventually reach the master system. Controlling the nonlinear systems and chaotic behaviors for achievement of finite-time synchronization is a very interesting topic [9,24]. Controlling the chaotic behaviors in order to achieve finite-time synchronization is a very interesting topic that has been considered in recent years [25].…”

Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for nth-Order Perturbed Nonlinear Systems

“…Theorem 1. Consider the n th -order nonlinear system (1) with external disturbance, tracking errors (2), switching function (3), and nonsingular terminal sliding surface (5). If the control signal is designed as…”

“…Moreover, considering the global stability and not paying attention to issues such as stimulus saturation and the validity region of state variables is another challenge in this field. In practical applications, actuator saturation is one of the most common nonlinear control inputs encountered in system design [5][6][7]. In particular, the presence of input constraints as a symbol of the physical limitations of control capacity is unavoidable in most stimuli.…”

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

“…Since Lorenz established chaos theory in 1963, research on chaotic systems has had a considerable practical impact [1]. Chaos phenomena in nonlinear domical systems have been widely used in science, engineering, and applied mathematics over the last few decades [2]. In fact, the most real systems in the world are nonlinear systems, but a chaotic phenomenon occurs when a deterministic system exhibits unusual exhibitions of aperiodic trajectories [3,4].…”