Projective Synchronization Of Different Fractional Order Chaotic Systems

Chaos is a certain form of exercise but can not be predicted, the highly sensitive natureof its initial value is known. Chaos sport everywhere, in real life, the most typical one is theweather changes, expressed in the chaos of this phenomenon since the Lorentz ProfessorChaos to create a one of the "butterfly effect" since the beginning of Chaos generated stronginterest. Found of chaos and chaotic create, became the third major breakthrough followingthe theory of relativity and quantum theory physics.Fractional calculus as an important branchof the theory of the calculus, due to the lack of practical application background, itsdevelopment is extremely slow. Until recent decades, it was found that the fractional chaoticsystems can still show chaotic behavior, and the operator is more accurate in describing thedynamic characteristics of the actual system, the use of fractional calculus. Since then, thestudy of fractional order chaotic systems has caused a high degree of attention of manyexperts and scholars.1999, Mainieri and Rehacek first jointly proposed the term projectivesynchronization, such synchronization exists in the scale factor, both the drive system andresponse system is phase-locked, but also can make them corresponding to the amplitude ofthe press of afixed percentage of synchronization. Secure communication features than thecolumn can be a binary number to be extended to M-ary number, in order to achieve fastertransfer projection also known for its synchronization in secure communication, high securityand high transmission speed, causing a number of scholars attention.For the current research status of the above areas, mainly as follows:First, based on Lyapunov stability theory, and the fractional stability theory and thenature of the fractional nonlinear systems, and fractional state-space model, used to determinethe fractional order chaotic systems is the stability of the new decisiontheorem, the stabilitytheorem to avoid the problem of solving the fractional equilibrium point and the Lyapunovexponent, which can easily select a control law, given a rigorous mathematical proof process,and through the self-structure of the Chen system synchronization control to verify thethecorrectness and feasibility of the theory. Secondly, the definition of the generalized projectivesynchronization of the stability theorem to projective synchronization of fractional Lorenzchaotic system and fractional-order Liu chaotic system, as well as four-dimensionalhyperchaotic fractional system, to achieve different fractionalProjective synchronization of chaotic systems. The results of numerical simulation to achieve the desired effect, in therealization of the different structure of projective synchronization, but also to prove theuniversal applicability of this stability theorem.Finally, on the basis of the results of the study, based on active control law, designed adifferent structure projection synchronous controller, the controller also has to select aconvenient, simple structure, and the fractional-order Liu system with fractional Lorenzsystemfor the control of the object, the use of estimates-the correction method of thefractional order hyperchaotic system Matlab numerical simulation, the simulation resultsshow that the controller enables two different structures of fractional order chaotic systems insynchronization to prove that the controllerthe effectiveness and operability.