Synchronizations Between Two Classes Of Fractional-order Chaotic Systems

Chaos is ubiquitous in nature and social sciences. Since the early 20th century,as one of the important subdisciplines in nonlinear sciences, chaos theory has attracted the attention of many scholars and has become a research hotspot in the area of nonlinear sciences. Chaotic systems are extremely sensitive to the initial conditions and can not be predicted, so it has huge value in the field of biology, chemistry, medical science, electronics, information science and secure communication. So far, the stability theory of the integer-order chaotic system tends to be mature and the synchronization approach of integer-order chaotic system has been deeply studied.However, the study of fractional-order chaotic system starts late and is not mature in theory. Although some achievements have been made, the development of fractional-order chaotic system is far behind that of integer-order chaotic systems. The main contents of this dissertation include:â‘  The background knowledge of chaos, chaos synchronization and the synchronization of fractional-order chaotic system are introduced.â‘¡ The basic theory of fractional calculus and Lyapunov stability are introduced. Also, the methods of chaos synchronization are introduced.â‘¢ Adaptive synchronization of fractional-order chaotic systems with uncertain parameters and parameter identification is discussed. A general method of designing controller for synchronization and parameter identification of fractional-order chaotic systems with uncertain parameters is proposed. The method is based on Lyapunov stability theory and stability theory of fractional-order chaotic systems. It realizes the adaptive synchronization between chaotic systems and identification of uncertain parameters. Furthermore, some basic chaotic dynamical behaviors of a new 4D fractional-order chaotic system are analyzed. Numerical simulation shows the effectiveness of the method.â‘£ Synchronization between two fractional-order chaotic systems with diverse structures and the same dimension is discussed. A general method of designing controller for synchronization and parameter identification of fractional-order chaotic systems with uncertain parameters is proposed. The method is based on Lyapunov stability theory and stability theory of fractional-order chaotic systems. It realizes the synchronization between chaotic systems with diverse structures and identification of uncertain parameters. Furthermore, some basic chaotic dynamical behaviors of the hyperchaotic Lorenz system and the hyperchaotic Lu fractional-order system are analyzed. Numerical simulation shows the effectiveness of the method.