Synchronization Of Chaotic System And Its Application Research In Secure Communication

Chaos is a special moving form of nonlinear dynamics system, it exists widely in nature, such as physics,chemistry,biology,geology and other social or technical sciences. Chaotic signal has the properties of continuous broadband power spectra,ergodic,noise like etc, these properties makes the study of chaos theory and its application research in secure communication become an advanced subject in scientific and engineering fields. It develops a new research field for the traditional theory of communication, it also provides a broad application stage for nonlinear science. Based on Lyapunov stability theory, this dissertation is concerned with the synchronization problem of nonlinear dynamical systems by using Schur complement lemma, Rayleigh inequality and Delay-dividing approach. Combined with secure communications, a secure scheme based on chaotic neural networks system is studied, also the signal transmission is realized.The main contributions of this dissertation are as follows:1 Synchronization of a class of chaotic systems with noise disturbances is discussed. Using schur complement lemma and Rayleigh inequality, a criterion is obtained that guarantees stability of this chaotic error system by constructing an appropriate Lyapunov function and designing a reasonable feedback controller. Finally, the scheme is applied to simulation example, the simulation results shows that the controller could handling noise very well, and the chaotic system will be synchronizaed.2 Robust H_∞synchronization of chaotic Lur'e systems is analyzed. Based on the principle of observer control, a new Lyapunov functional is created. Although using the Leibniz-Newton formula and the integral inequality, a delay-dependent condition is obtained under which the chaotic systems are robustly synchronized by delay-dividing approach. An illustrative example demonstrates that our method can give less conservative results comparing to the existing methods.3 Synchronization of a class of chaotic neural network is studied, and the global asymptotic synchronization condition of this class of system is obtained. Also its application in communication is explored. Based on chaotic masking and chaotic shift keying, the initial signal is modulated to be a sine wave and is divided into two parts. By using the hidden switch between different neural network, every part transmitted in the Cellular and Hopfield neural systems respectively. Computer Simulation shows that the obtained results are feasible and valid.