Projective Synchronization Of Several Sets Of Fractional-order Chaotic Systems

Fractional calculus as a classic of mathematical concepts since the17th century known by people, but it has not been widely used in many areas of life. In recent decades, fractional calculus was found for a changed and better help us to know what we know of the nature of the potential role and it has began to be widely used in some fields of science such as engineering, physical, mathematical biology, economics and finances and so on.Chaos and chaos synchronization as important areas of research of dynamics systems has attracted great interest, but for a long time research has been emphasis on integer order systems, research on chaos and chaotic synchronization for fractional order systems are still rare. To currently, people has research many types of chaos synchronization, including full synchronization, phase synchronization, lag synchronization, projective synchronization, which projective synchronization is one of the most worth note of chaos synchronization because projective synchronization of the two state variables can be synchronized to a single scale factor, this a characteristics for confidential communications in the put binary into M-binary, this feature is used to secure communication to increase transfer speeds with great prospects.Chaos and projective synchronization in fractional-order dynamics systems of people did a lot of work, but there are still some typical fractional-order systems of chaos and projective synchronization has no cause for concern. This paper mainly studies some systems that some people have not studied, such as incommensurate fractional-order hybrid optical system, a new type of commensurate fractional-order autonomous system, as well as fractional-order hyper-chaotic T system, chaos and projective synchronization for those fractional-order systems is the focus of this paper. The organizational structure of this paper is as follows:In the first chapter, we mainly introduces the fractional calculus and fractional-order chaotic system and chaotic synchronization of the historical background and some fundamental knowledge of this article needs are given.In the second chapter, we mainly research the chaos of incommensurate fractional-order hybrid optical system use maximum Lyapunov exponent and study of projective synchronization of commensurate fractional-order hybrid optical system and incommensurate fractional-order hybrid optical system uses a ingenious control method.In the third chapter we major research the chaos in a new kind of commensurate fractional-order autonomous system and fractional Laplace transform has been used to achieve projective synchronization of commensurate fractional-order hybrid optical system and this new kind of commensurate fractional-order autonomous system.In the forth chapter we major research the chaos in hyper-chaotic of integer order and fractional-order T system, a novel control method has been used to achieve projective synchronization of fractional-order hyper-chaotic T system and fractional-order hyper-chaotic Lu system.