Exponential synchronization of fractional-order complex chaotic systems and its application

Abstract

In this article, exponential synchronization between fractional order chaotic systems has been studied by using exponential stability theorem. The stability analysis has been done with help of an existing lemma, which is given for Lyapunov function for fractional order system. The fractional order complex chaotic systems viz., Lorenz and Lu systems are considered to illustrate the exponential synchronization. The numerical simulation results are presented through graphical plots to verify the effectiveness and reliability of exponential synchronization. The application in communication through digital cryptography is also discussed between the sender (transmitter) and receiver using the exponential synchronization. A well secured key system of a message is obtained in a systematic way.