Multi-State Synchronization of Chaotic Systems with Distributed Fractional Order Derivatives and Its Application in Secure Communications

Abstract

This study investigates multiple synchronizations of distributed fractional-order chaotic systems. These systems consider unknown parameters, disturbance, and time delays. A robust adaptive control method is designed for multistage distributed fractional-order chaotic systems. In this paper, system parameters are changed step by step. Using Lyapunov’s function, while the synchronization error convergence to zero is guaranteed, adaptive rules are designed to estimate the parameters. Then, a secure communication scheme is proposed using the new chaotic masking method. Finally, the simulations are performed on a chaotic system of distributed Duffing fractional order. The results show the high efficiency of the proposed synchronization scheme using robust adaptive control, despite the parametric uncertainties, external disturbance, and variable and unknown time delays. Then, the simulations were performed on the sinusoidal signals of the message in the application of secure communications. The results showed the success of the proposed masking scheme with synchronization in coding and decoding information.

Designing a Secure Mechanism for Image Transferring System Based on Uncertain Fractional Order Chaotic Systems and NLFPID Sliding Mode Controller

“…Despite the uncertainties and time delays in the system, the fractional order chaotic master and slave systems were entirely synchronized according to the proposed mechanism, the details of which were described in the previous section. Images were encrypted using the [27] algorithm in this section. The encrypted image was then transmitted using fractional order chaotic masking and received with high precision before being decoded.…”

“…Various statistical parameters, including the histogram difference between the original image and the restored image, correlation, NPCR, PSNR, and information entropy, were calculated for standard color benchmark images and medical color images to demonstrate the efficacy of the proposed method. These parameters are standard criteria that have been used in numerous articles [27].…”