Delay Synchronization Of Chaotic Systems And Circuit Simulation

Time delay chaotic system is an infinite dimension system, it can be a hyperchaotic system with large numbers of positive Lyapunov exponents. This syetem can generate highly stochastic and unpredictable time series, what makes it has the great potential of application in secure communication. Chaotic synchronization is a key technology for chaotic security communication. Nevertheless, there is still a large distance between the chaotic theory and engineering application. Time-delayed chaotic systems as study object, the main contributions of the thesis are as follows:(1)Introducing delayed time into known chaos systems to construct new time-delayed systems. Routh stability criterion in basic principles of automatic control was firstly introduced to the stability analysis of delay-dependent systems, and the analytic procedure of a chaotic system with certain parameters was presented.(2)Using modern control technology, chaos synchronization of delayed differential equations was designed and analyzed. Sufficient conditions of asymptotical synchronization were proposed by using Lyapunov-krasovskii functional theory. At last we realized secure communication application by means of the audio signal, and the experiment had showed the the ability to resist disturbance of the design.(3)For the sake of enhancement of chaos in nonlinear system, an electronic circuit of advanced time delay Lorenz system was designed by using Multisim. It has chaos-like behavior, and accordances with the results of simulations.(4) Synchronous control of the driving system and response systems, matching the certain coupling coefficient based on the time-delayed systems, was realized in this paper. Then, we designed the control circuit of two high-dimensional time-delayed chaotic systems, and simulated the circuit on the simulation software Multisim.Based on the constructed time delay chaotic system, an implementation of chaos synchronization is well proposed. The proposed circuit which enhances the chaos in nonlinear system could be used as chaos generator, and has potential applications to signal processing and communications. The control circuit simulation confirms the effectiveness of the synchronous method,and the simulation can realize the synchronous contorl according to the coupling ratio of demand.