Chaos in fractional-order discrete neural networks with application to image encryption.

In this paper, a three-dimensional fractional-order (FO) discrete Hopfield neural network (FODHNN) in the left Caputo discrete delta's sense is proposed, the dynamic behavior and synchronization of FODHNN are studied, and the system is applied to image encryption. First, FODHNN is shown to exhibit rich nonlinear dynamics behaviors. Phase portraits, bifurcation diagrams and Lyapunov exponents are carried out to verify chaotic dynamics in this system. Moreover, by using stability theorem of FO discrete linear systems, a suitable control scheme is designed to achieve synchronization of the FODHNN. Finally, image encryption system based on the chaotic FODHNN is presented. Some security analysis and tests are given to show the effective of the encryption system.