The Projective Synchronization Of Fractional-order Chaotic System

The theory of fractional-order calculus is a classical mathematical notion, with a history as long as calculus itself. Although it has so long a history, its applications to physics and engineering are just a recent subject of interest. It has been found that in interdisciplinary fields, many systems can be described by fractional differential equations, such as electromagnetic wave, electrode-electrolyte polarization, dielectric polarization and viscoelastic system.Since the pioneering work of Pecora and Carroll synchronizing identical chaotic systems with different initial conditions? chaos synchronization has become a sub-ject of great interest. Up to now, a variety of approaches have been proposed for the synchronization of chaotic system which include complete synchronization, phase synchronization, generalized synchronization, lag synchronization and projective synchronization. Among all the kinds of chaos synchronization, projective synchro-nization is one of the most noticeable problems because of its proportionality be-tween the synchronized dynamical states. In applications to secure communications, this feature can be used to extend binary digital to M-nary digital communication for achieving faster communication. Recently, the concept of projective synchro-nization is extended to generalize projective synchronization, modified projective synchronization and hybrid projective synchronization.However, most of the existing papers discuss chaotic synchronization methods mainly focus on the integer-order chaotic systems. To the best of our knowledge, there is little information about the synchronization of fractional-order chaotic sys-tems. Motivated by the above discussion, in this thesis, the projective synchroniza-tion of fractional-order chaotic systems is investigated. The outline of the rest of the thesis is organized as follows:In the first chapter, some background knowledge of chaotic synchronization, fractional-order calculus and the preliminary knowledge which is necessary in the paper are given.In the second chapter, we study general projection synchronization between same dimensional chaotic dynamical systems by using active control.In chapter3, we study modified projective synchronization between different dimensional chaotic dynamical systems by using added-order and reduced-order schemes.In chapter4, we study general hybrid dislocated projective synchronization between fractional-order chaotic systems and integer chaotic systems.