Research On Synchronization Of Fractional-order Chaotic Systems

In the field of nonlinear,the chaotic phenomenon has been studied.In order to get rid of the harmful ingredients in the chaos,the concept of control and synchronization of chaos have been proposed,and there are a lot of valuable research results in many practical control methods at present.However,with the introduction of fractional calculus,due to the more complex dynamic characteristics of fractional-order chaotic systems,it has a broad application prospect in the field of signal encryption and system security.In this paper,the properties of the fractional-order multi-scroll Colpitts chaotic system and the fractional-order Bao system,and the influence of parameters on these chaotic motions of systems are analyzed in detail.By numerical simulation,the range of the order number and parameters is computed when the system is in a chaotic state.It is discovered that the fractional-order chaotic systems have many different states of motion.The fractional-order multi-scroll Colpitts system is in a chaotic state,the chaotic attractor exists a special transformation from a single scroll to multi-scroll.The fractional-order Bao system has a complex phenomena of presenting periodic and quasi periodic states alternately.By using the adaptive synchronization method,in the case of uncertain parameters,the synchronization of fractional-order multi-scroll Colpitts chaotic system are studied in same order and different order.Through the design of controller and parameter adaptive law,the drive system is synchronizing with the response system and identifying uncertain parameters.Using the feedback synchronization method,designing feedback variables,synchronization of fractional-order Bao system with the same structure and the different structure are researched and the two systems converge in the same order.By numerical simulation,it is cleared that these two synchronization schemes can be used to fractional-order chaotic systems.Based on the circuit theory,designing circuits of the fractional-order chaotic systems,constructing circuit models,setting the parameters of the components.Finally,simulating by Multisim,the circuit simulation results are in agreement with the numerical results.