Chapter 21 - On the Synchronization and Recurrence of Fractional Order Chaotic Systems

Abstract

It has long been recognized that many chaotic systems are known to display fractional order dynamics. Many authors start to investigate the chaotic dynamics of fractional order dynamical systems for variant economical and technical applications. A recent focus of interest on the chaos control of several fractional order chaotic systems was mentioned. On the first hand, it is shown that the majority of fractional order systems can produce a chaotic attractor if their orders are strictly less than three. On the other hand, it demonstrated that these fractional order chaotic systems can be coupled and also synchronized. However, the chaos control and chaos synchronization of both the fractional order Lorenz’s system and the fractional order Rössler’s system were investigated separately by using classical methods, but the presented results in these two areas were unfortunately limited and not precise for many reasons.