Search

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.

This paper investigates the robust adaptive synchronization of multi-mode fractional-order chaotic systems (MMFOCS). To that end, synchronization was performed with unknown parameters, unknown time delays, the presence of disturbance, and uncertainty with the unknown boundary. The convergence of the synchronization error to zero was guaranteed using the Lyapunov function. Additionally, the control rules were extracted as explicit continuous functions. An image encryption approach was proposed based on maps with time-dependent coding for secure communication. The simulations indicated the effectiveness of the proposed design regarding the suitability of the parameters, the convergence of errors, and robustness. Subsequently, the presented method was applied to fractional-order Chen systems and was encrypted using the chaotic masking of different benchmark images. The results indicated the desirable performance of the proposed method in encrypting the benchmark images.

In this paper, a novel medical image encryption method based on multi-mode synchronization of hyper-chaotic systems is presented. The synchronization of hyper-chaotic systems is of great significance in secure communication tasks such as encryption of images. Multi-mode synchronization is a novel and highly complex issue, especially if there is uncertainty and disturbance. In this work, an adaptive-robust controller is designed for multimode synchronized chaotic systems with variable and unknown parameters, despite the bounded disturbance and uncertainty with a known function in two modes. In the first case, it is a main system with some response systems, and in the second case, it is a circular synchronization. Using theorems it is proved that the two synchronization methods are equivalent. Our results show that, we are able to obtain the convergence of synchronization error and parameter estimation error to zero using Lyapunov’s method. The new laws to update time-varying parameters, estimating disturbance and uncertainty bounds are proposed such that stability of system is guaranteed. To assess the performance of the proposed synchronization method, various statistical analyzes were carried out on the encrypted medical images and standard benchmark images. The results show effective performance of the proposed synchronization technique in the medical images encryption for telemedicine application.

In this paper, the multi-state synchronization of chaotic systems with non-identical, unknown, and time-varying delay in the presence of external perturbations and parametric uncertainties was studied. The presence of unknown delays, unknown bounds of disturbance and uncertainty, as well as changes in system parameters complicate the determination of control function and synchronization. During a synchronization scheme using a robust-adaptive control procedure with the help of the Lyapunov stability theorem, the errors converged to zero, and the updating rules were set to estimate the system parameters and delays. To investigate the performance of the proposed design, simulations have been carried out on two Chen hyper-chaotic systems as the slave and one Chua hyper-chaotic system as the master. Our results showed that the proposed controller outperformed the state-of-the-art techniques in terms of convergence speed of synchronization, parameter estimation, and delay estimation processes. The parameters and time delays were achieved with appropriate approximation. Finally, secure communication was realized with a chaotic masking method, and our results revealed the effectiveness of the proposed method in secure telecommunications.