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Synchronization of a Class of Chaotic Systems

Author: FanBing
Tutor: WangXingYuan
School: Dalian University of Technology
Course: Applied Computer Technology
Keywords: Chaos Synchronization Lyapunov stability theory Hyperchaotic system State observer
CLC: O415.5
Type: Master's thesis
Year: 2011
Downloads: 136
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Abstract


As an important part of the non-linear disciplines, chaos theory in secure communications and many other fields has great application prospects. Compared with the low-dimensional chaotic system, hyper-chaotic system at least in the four-dimensional and higher dimensional nonlinear systems with two or more positive Lyapunov exponent, a higher level of confidentiality and anti-breaking ability, more practical . Therefore, research in this area in recent years has aroused widespread concern. Considered in the current research is the same structure as the chaotic system synchronization problem between the practical application can sometimes be related to the different structural systems, heterogeneous systems has gradually become a research hotspot. In this paper, the combination of theoretical analysis and numerical simulation, several typical chaotic system synchronization method: parameters are known and unknown of Lu chaotic system control and synchronization issues. Based on Lyapunov stability theory, design adaptive controller. Strict mathematical theory that the controller can control the parameters are known and unknown Lu chaotic system to achieve stability, but also to make it self-synchronization. The combination of Lyapunov stability theory and to activate control theory, given theoretically Lu chaotic system using linear feedback method, nonlinear feedback and active control to achieve a sufficient condition for self-synchronizing. Based on state observer, the design of a class of chaotic systems Generalized projective synchronization scheme, and proved the correctness of this theory. This method does not need to calculate the Lyapunov index, to avoid the computational complexity. In the numerical simulation hyperchaotic Lu system and hyperchaotic Rossler system as an example. Adaptive global hybrid projective synchronization between two identical or different dimension heterogeneous chaotic systems. With parameter identification adaptive global hybrid projective synchronization program, and based on Lyapunov stability theory that the program will enable the two of the same dimension heterogeneous chaotic systems global hybrid projective synchronization, and extended through the system heterogeneous chaotic system also allows two different dimensions of global hybrid projective synchronization. In the numerical simulation, the corresponding chaotic system to verify the proposed scheme of the same dimension (Lorenz and Chen-lee system) and different dimensions (hyperchaotic the LU system and Chen system, Lu system and hyperchaotic Rossler system) chaotic system the Adaptive Global Hybrid Projective Synchronization validity.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Nonlinear physics > Chaos Theory
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