| Knowledge on chaos is one of important achievements in nonlinear science. Theconcept of synchronization chaos is to make two chaotic systems oscillate in asynchronized manner, where in the chaotic motion is now developed so as the twosystems are in step during the course of time. Since drive-response synchronizationwas first found by Pecora and Carroll in early 1990s, synchronization of chaoticsystems has attracted significant interests due to its potential application in manyareas of science and technology such as communication, electronics.The dissertation studies the chaotic characters and analyzes the ways of designingimpulsive synchronization, basing on the theory of nonlinear control and stabilityanalyze. Then combining both conventional cryptographic method and impulsivesynchronization of chaotic systems, we propose a new chaotic secure communicationscheme. We use this new chaotic secure communication scheme to transmit a speechsignal, to improve the efficiency of channel usage and secure capability.In part of impulsive synchronization design and laws, we have considered the problemof impulsive control based on the theory of impulsive differential equations. Somesufficient conditions were derived to ensure the asymptotic stability of an impulsive differentialsystem. The results are also applied to design an impulsive control for a class ofnonlinear systems. We also present a theory of impulsive synchronization of two chaoticsystems. A linear impulsive feedback synchronization rule is proposed according tosynchronization errors. The condition of synchronization asymptotic stability of therule; namely, an estimation of the impulse interval is given. Simulation results basedon a typical chaotic system; namely, Chua's oscillator, are provided, to show therobustness of the impulsive synchronization to additive noise. When △= 0.002 inthe strong coupling and △= 3×10-4 in the strong coupling, system asymptoticallyapproaches the origin with a synchronization time of about 0.05. |
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