Dissertation > Mathematical sciences and chemical > Physics > Theoretical Physics > Nonlinear physics > Chaos Theory

Based on active control method unified chaotic system synchronization

Author YangYang
Tutor CaiShaoHong
School Guizhou University
Course Theoretical Physics
Keywords chaos chaotic synchronization Unified chaotic system Runge-Kutta method
CLC O415.5
Type Master's thesis
Year 2007
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The study on chaos phenomenon is one of the important subjects in nonlinear science. The chaos means that the determinacy system produces similar to stochastic motion, and it seems that there are not rules at all but have certain laws. Chaotic synchronization means that the motion trajectories of two systems line prone to the same value finally (completely synchronization). Chaos has the sensitiveness characteristic for initial value, and its signals have、Pseudo-random characteristic, etc. So the applications of chaotic synchronization in other fields, especially in secure communication, cause people’s extensive concern.The chaotic synchronization problems of the continuously changingsystem---unified chaotic system are discussed in this paper, inconnection with one parameter, which are proposed by Chen Guanrong, Lu Jinhu, etc. With the parameter changing, Unified chaotic system includes Lorenz system、Lu system、Chen’s system three kinds of structure, offering the new model and thinking for people to study chaos and its synchronization control. This text summarizes chaotic synchronization methods of unified chaotic system which are Commonly used at present, such as unified chaotic system coupled synchronization, Feedback synchronization, etc. Although these methods can be realized, the derivations are extremely complicated, and it is difficult to realize in physics. We apply the active control methods in unified chaotic system study. The main characteristics of active control synchronization method are simple and actual, and that the dominating function are realized easily in physics, having stronger application value. The analysis results of the theory indicate that unified chaotic system can realize synchronization under certain parameter condition, simulating by fourth order Runge-Kutta method on computer at the same time. The simulation result indicates that the theory result keeps the same with imitating experiment for isomorphism condition.The innovation of this text: First, expanding active control method from lower order chaotic synchronization to higher order chaotic synchronization. Second, this method are applied in synchronization study of unified chaotic system, and the theory analyzes are combined with numerical simulation, receiving the theory result and emulation result.Through the analysis of this text, we have a deeper understanding for chaotic synchronization control. This method is general, and the algorithm is simple. It is not necessary to calculate Lyapunov exponent or Lyapunov function. This method is realized easily in physics, improving the possibility of practical application.

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