| Study of theories and applications of fractional chaotic systems is a hot topic in the field of nonlinear science. Taking the fractional unified systems as the model, adopting the methods of theory analysis and numerical simulation, the dynamic characteristic, synchronization control and its application of fractional unified chaotic system are studied.A dynamic simulation new method to analyze fractional-order systems is discussed. By designing the fractional-order differential operator simulation model, and setting up fractional-order chaotic system simulation model, the procedure of system variables evolvement can be observed dynamically, and the dynamic characteristics of fractional-order system can be analysised by utilizing the simulation data. It provides a new way to study the fractional-order system.By observing attractors phase diagrams, calculating power spectral density and the largest Lyapunov exponent, the dynamic characteristics of fractional-order unified 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 unified system is piece-wise chaotic with the fixed or changed system parameter. It lays a theoretical foundation for the applications of fractional unified chaotic systems.Synchronization control of two fractional-order unified systems with different initial value is studied by adopting the approaches of drive-response synchronization and co-coupled synchronization. The simulation results display the synchronous system has good robustness to parameters and synchronous performances. It provides a technical foundation for the applications of fractional chaotic systems.Based on the chaotic masking and chaotic keying methods, the security communication systems of fractional unified chaotic systems are set up. Simulation experiments and the performances analysis of this system are finished. The results show that the fractional secure system has good security. |
PDF Full Text Request