On Synchronization Of Chaotic System And Its Application In Secure Communication

Chaos is a special nonlinear dynamics system, whose trajectory of the orbits in the phase plane is very complex, random, and can be observed in fairly simple dynamical systems. Chaotic signal is ergodic, non-periodic and noisy like with continuous broadband power spectra etc. These properties coincide with the requirements for signals are applied in secure communication systems. Along with the appearance of chaotic synchronization methods, synchronization of chaotic system and its applications in secure communication have aroused the greatest attention to researchers. Recently it is becoming the hottest and difficult subject for the researchers to find a suitable synchronization scheme.Based on the theories of nonlinear control and stability analysis, some design and improvement on chaotic synchronization are studied and based on these proposed results, the synchronized systems are applied in secure communication. The main contributions of this dissertation are as follows:Firstly, synchronization on different azimuth-rotating is investigated. With the help of Lyapunov stability theory, considered the stationary and mutative angle, the corresponding controllers are designed. And the validity and feasibility are illustrated via theoretical analysis and numerical simulations. Some conclusions are derived from the chaos synchronization techniques. For one thing, synchronization of two arbitrary nonlinear chaotic systems according to different azimuth can be realized. For another thing, projective synchronization, complete synchronization and anti-synchronization are special cases of rotating synchronization. Namely, synchronization on different azimuth-rotating is more general and universal. Thus, the application field of rotating synchronization is much wider. Better chaotic secure communication can be assured based on chaotic masking technology.Secondly, the synchronization of complex chaotic systems is studied. This synchronization of imaginary part and the real part are achieved respectively. The synchronization of the imaginary part is transformed into the real domain to analyze. State feedback controller can be easily achieved so that the response system converges to the output of the drive system as time increases. In fact, this synchronization still is the synchronization of real system. According to the characteristic of the complex chaotic system, the module and phase synchronization instead of imaginary part and real part in complex system is studied. With some advantages of increasing the transmission capacity of the complex chaotic system signal, enhancing transmission secrecy, and recovering effective signal in a short time, the complex chaotic system can be used in secure communication effectively. The normal and effective secure communication is ensured.Thirdly, synchronization of time-delayed bidirectional coupled chaotic systems and complex chaotic systems with unknown parameters are studied. The update rate of unknown parameters and the intensity rate of coupling coefficients are given for the synchronization. Numerical simulations are presented to illustrate the chaos synchronization in a short time. The scheme of the two systems synchronization is very useful in secure communication.Finally, the conclusion is given and some open problems are also discussed.