Synchronization Control Of Fractional Order Chaotic Systems

Chaotic systems have several unique characteristics,such as complex dynamics,sensitive to initial conditions and unpredictable future behavior.Recently,many scholars at home and abroad have gain more interested on studying chaotic synchronization and its applications.Numerous new chaotic system models have been proposed and validated.The results had explored both low-dimensional chaotic systems and high-dimensional chaotic systems.Researchers commence to utilize fractional calculus to further analyses chaos,such as,proposed fractional chaotic system,and integrated chaos with other disciplines to study the application of chaos.Currently,chaos has explored practical applications in image encryption,communication encryption,fault detection and various other fields.The main research work of current study is as follows:(?)A new three-dimensional autonomous chaotic system is proposed.The new three-dimensional chaotic system consists of four parameter constants and three non-linear terms.Through theoretical analysis and numerical calculation,the basic dynamic characteristics of the three-dimensional chaotic system,such as Lyapunov exponential spectrum,Poincar_section and bifurcation diagram,were analyzed and studied.The analog circuit of the chaotic system was designed and simulated with Multisim software.The simulation results showed that the chaotic system is not topologically equivalent to the previous chaotic system.Compared with other chaotic systems,the phase diagrams of the new system are asymmetric,and its motion characteristics are complex and disordered.The hardware circuit of the system was built,and the phase diagrams were in good accordance to the theoretical analysis,which proves the accuracy and efficiency of the new chaotic system.Finally,the synchronization of two new chaotic circuit systems is realized by coupling feedback synchronization method,which lays a foundation for the application of the new chaotic circuit theory.(?)On the basis of integer order new chaotic system,a new fractional order chaotic system has further constructed and its chaotic characteristics has studied.Initially,the phase trajectory of the fractional-order chaotic system is plotted based on the predictor-corrector time-domain method,and the circuit of the 2.7-order chaotic system is designed and implemented by the frequency-domain approximation method of the baud chart.The results have exploited that the system was functional and effective.The numerical simulation and circuit design show that the system has chaotic attractors in a certain range of parameters.On this basis,the synchronization of the fractional-order chaotic system was studied.The synchronization of the fractional-order chaotic system is realized by feedback synchronizationmethod,and the synchronization of two fractional-order chaotic systems was realized by electronic circuit.(?)Based on the new fractional chaotic synchronization circuit,a chaotic secure communication circuit was designed.The chaotic secure communication system uses the chaotic masking secure communication scheme to encrypt the information signal.The main idea of current study was conducted to understand the superposition of the information signal and the chaotic signal by the operational amplifier inverse additive operation circuit,to obtain the mixed chaotic signal of the inverse phase,and then to use the inverter to reverse the phase.Finally,the mixed chaotic signal was subtracted from the chaotic signal by subtraction operation circuit,and the information signal was obtained.The sender and the receiver were synchronized to encrypt the signal.In summary,through the research of integer and fractional chaotic circuit theory and electronic circuit,the design and application from theory to hardware circuit were studied that provided a new research prospect for future chaotic circuit.