Images encryption based on robust multi-mode finite time synchronization of fractional-order hyper-chaotic Rikitake systems

The main goal of this paper is to design a finite time multiple synchronization controller for fractional order hyper chaotic Rikitate systems. In this article, systems are considered with unknown delays and unknown parameters and synchronization is performed in the presence of disturbance and uncertainty. In the proposed method, adaptive rules for estimating unknown parameters, disturbance bounds and uncertainties as well as control efforts for synchronization in finite time are obtained with the help of Lyapunov's stability theorem. Synchronization errors have converged to zero in finite time. Also, the encryption performance of images and their transmission was investigated based on the proposed multi-mode synchronization algorithm. Additionally, the histogram diagram of several encrypted images was shown based on the synchronization techniques of the fractional-order Rikitake system. A number of statistical parameters including histogram, correlation, NPCR, UACI, PSNR, and information entropy were calculated for the encrypted images in order to indicate the performance and compare the two proposed synchronization methods. Finally, satisfactory results in different image encryption were achieved based on the synchronization technique of the fractional-order Rikitake chaotic system.