The Analysis and Application on a Fractional-Order Chaotic System

Abstract

An integral-order hyperchaotic system with four-dimension is expanded to be a fractional-order system whose chaotic behaviors are analyzed, Firstly, based on the stability theory of fractional-order linear system and the thinking of tracking control, a synchronization method for two fractional-order systems with different structures is proposed, and an analytic expression for synchronization controller is given. Secondly, taking the extended fractional-order system and R?ssler hyperchaotic system as example, the synchronization between them is numerical simulated. Finally, the proposed synchronization method is applied to encrypt and decrypt digital images. The simulation results show that the lowest order that extended fractional-order system appears chaos is 3.2, and this method has many advantages for encrypting and decrypting digital images, such as sensitive secret keys, random uniform distribution of pixels and low correlation between adjacent pixels.