Synchronization Of Fractional-order Chaotic System Based On Direct Design Method

Although the study of fractional-order calculus has more than 300 years old history, its applications to engineering and physics has been attracted lots of attention just in the recent years. Many known chaotic systems display fractional-order dynamics behavior and therefore chaos synchronization of fractional-order chaotic system is the focus of recent researches.In this paper, we have studied synchronization of fractional-order chaotic systems using direct design methods. The content is divided into four parts. First, we gives the introduction of the predecessor's research work, including the concept of chaos, methods and research status of fractional-order chaotic systems. Second, the numerical simulation method in MATLAB and circuit simulation methods in EWB for realizing fractional-order chaotic systems are introduced. Furthermore, using linear feedback control approach, based on the stability theory of fractional-order systems, the synchronization methods for fractional-order chaotic systems are studied. The controller is simple. Three fractional-order chaotic systems and a new fractional-order hyper chaotic system are taken as examples to demonstrate the effectiveness of presented method. The last part proposes,a novel method of chaotic synchronization for the fractional-order chaotic systems based on ant symmetric structure. The method can be applied to solve synchronization problems of all of fractional-order chaotic systems, e.g., fractional-order Lorenz system, R osslersystem, Chen system, Liu system, Lüsystem and hyper chaotic Lorenz system.In general, we presented two novel methods of fractional-order chaotic synchronization based on the stability theory of the fractional-order systems. Both numerical simulation in MATLAB and circuit simulation in EWB results are shown to demonstrate the feasibility and effectiveness.