Synchronization and secure communication using some chaotic systems of fractional differential equations

Synchronization phenomenon has been studied intensively because of its application in many fields, and one of it is secure communication. There are many ways for synchronization, such as feedback method, adaptive techniques, time delay feedback approach, backstepping method, with nonlinear control [10]. We will prove here synchronization and anti-synchronization between two chaotic systems of differential equations, by considering a suitable nonlinear control function. In the first section we will show synchronization between some representative chaotic systems of fractional differential equations, coupled fractional systems T and between system T and Rössler system. In Section 2 we will present anti-synchronization of the same chaotic systems and we will compare the two methods. In Section 3 we will apply synchronization in secure communication. Numerical simulations are done using Adams-Bashforth-Moulton algorithm [4]. In last section some conclusions are presented. We will briefly give the definition of fractional derivative, of the following form