Studying Chaos And Synchronization Of A Fractional Order Four-Dimentional Dynamic System

Study of theories and applications of fractional chaotic systems is a hot topic in the field of nonlinear science.taking a new four-dimensional fractional order dynamic system as the model,adopting the methods of theory analysis and numerical simulation,the chaotic characteristic and synchronization control are studied.First of all, On the basis of the stable theory for fractional linear systems,it is given the theory about that the fractional order nonlinear chaotic system is chaotic .the numerical solution of fractional differential systems are given through the predictor-corrector algorithm with the identity of fractional derivativeSecondly, Adopting Matlab and numerical simulation ,it give attractors phase diagrams and calculat the Lyapunov exponent,the chaotic characteristic of fractional.order chaotic system are analyzed in detail。and the rule of appearing the chaotic states is discovered with both the parameter and the order.The fractional order chaotic system is periodic and hyperchaos with the fixed system parameter.It lays a theoretical foundation for the applications of fractional order chaotic systems.Thirdly, Synchronization control of two fractional-order unified systems with different initial value is studied by adopting the co-coupled synchronization.The simulation results display the synchronous system has synchronous performances.It provides a technical foundation for the applications of fractional chaotic systems.