Research On Chaos Synchronization And It's Application In Secure Communication

Chaotic motion is a complex nonlinear motion,whose trajectory of the orbits in the phase plane is very complex but not stochastic. The chaotic phenomena have been observed in a lot of real systems and the research on chaos has been focused on chaotic control and application now. Chaos control is necessary when the chaotic motion is produced and harmful to electrical and electronical systems. On the other hand,the dynamic properties of chaos signal such as ergodicity,aperodic,uncorrelated,broad band and noise-like have been proved to be useful of communication and pictrure crypt systems and in describing and diagnosing nonlinear dynamic systems. The complexity, singularity and wide potential application of chaotic dynamic systems make the research on the chaotic control and synchronization theory to be more challenging. The research in this field becomes a new research focus in nonlinear science fields.The main contents of this dissertation contain the analysis on control and synchronization of chaotic systems and the application in secure communication. The synchronization of chaotic systems has been attained by several mehtods,which are falled into two strategies: coupled synchronization and nonlinear feedback synchronization. The comprehensive overview of secure communication based on chaotic synchronization and the application of chaotic synchronization in secure communication are presented in this dissertation. In this dissertation,the main contributions are following:1 Based on the Chua's circuit, a kind of n-scroll chaos generator is studied deeply. The characteristics of the piecewise linearity in nonlinear part of the modified Chua's circuit are discussed. The 3-section nonlinear part is subsequently modified and extended to multi section nonlinear part, and the mathematic model of the generator is built. The simulation proved the anticipated purpose to generate n-scroll chaotic signal. Then the relationship between equilibrium points and number of scrolls are studied. Based on previous research, a general theorem to generate n-scroll chaos attractors is presented and discussed. This method is proved to be feasible to be applied in secure communications. Also the scalar properties of this system are studied.2 A deep study on a coupled"master-slave"chaotic synchronization system is made based on the Pecora-Carrol method and Lyapunov fucntion. The mathematic model is built and the simulation is made. Then, based on the mathematic simulation, the circuit model of the system is constructed. Also the simulations are made; At last, the real circuit boards are made in this dissertation. Through the observation of the oscillator's display, the anticipated results could be shown. The summary is made and a prediction of the feasibility of this system to be applied to the secure communication in the future is also discussed; The Phase Locked Loops have good capture properties and it's easy to be applied in real system. The PLL also can be applied in chaos synchronization by PC method. It is realized between two PLL driven by a master PLL. Simulation results are consistent with the theoretical analysis; Also, a chaos synchronization based on Lorenz system is given. The synchronization system is realized by simplify the Lorenz function with just one parameter. The feasibility of this system to be applied in secure communications is also discussed.3 Some previous chaos synchronization methods have been analyzed, based on which a chaos synchronization scheme is given using the nonlinear feedback theory. This method originates from Lyapunov function stability theory for the purpose of synchronization between coupled systems for any initial states. The Lorenz system and the modified Chua's circuits are also applied by this theory. The process deduction proves more effective using this method compared with projective synchronization. Simulation results show the feasibility of this system to be applied in secure communications; Then for the modified Chua's circuit, using one parameter nonlinear feedback method to analyze two modified Chua's circuit and the feedback gain limits is calculated by Hurwitz stability. The nonlinear feedback controller is designed. At the same time, the synchronization problem when the parameters are out of the limits are also considered. The simulation results and the simulation circuits board are given. The simulation results proves that the nonlinear feedback controller has simple structure and easy to be realized and very feasible for secure communications.4 Based on convolution method, a synchronization method between two discret time systems is given. Using cascaded structure, the modulation and demodulation are unified. Then a novel chaos generator is given. It has stable chaotic characteristic which is independent of input signals. The new system uses the nonlinear digital filters and oscillators. The system model diagram is built. After deep analysis and deduction, based on the system structure, the simulation model of the system is constructed and the simulations are made. The simulation results are consilient with the previous analysis quite well. A prediction of the feasibility of this system to be applied to the secure communication in the future is given. 5 The proportion of chaos signals and the information signals is very important in secure communications by chaos mask. Based on coupled chaos synchronization, the power spectrum of chaos signals and information signals are deeply studied for chaos mask. The simulation results are given and analyzed; The chaos sequence code is also studied deeply in discrete time systems, especially for Logistic and Chebyshev sequences. They are studied and compared in terms of autocorrelation, cross-correlation, mean squre value of autocorrelation and root-mean-squre value of cross-correlation. The results proves that the two codes are applicable for chaos codes; To increase the channel utilization and save channel resources, a secure communicaiton based on channel TDM is presented. The slot assignment is the key problem in this system. The problem is studied deeply and analyzed. The simulation results proves the solution feasible; Mismatch degree of parameters in chaos sycnhronization systems are very important section in secure communications. Based on the modified Chua's circuit, the mismatch is studied and discussed deeply. Through calculation, the impact of the mismatch of every parameter in the system is analyzed and discussed.