The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications
碩士 === 國立新竹教育大學 === 人資處數學教育碩士班 === 99 === Networks of coupled chaotic oscillators model many systems of interest in physics, electrical engineering, biology, laser systems, etc. In particular, complete chaotic synchronization, all oscillators acquiring identical chaotic behavior, has received much a...
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ndltd-TW-099NHCT54800132016-04-11T04:22:39Z http://ndltd.ncl.edu.tw/handle/73763588223852880290 The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications 小波變換方法對於一種非對稱稀疏型耦合矩陣的固有值問題與其同步化之應用 Chun-Kai Hsu 許竣凱 碩士 國立新竹教育大學 人資處數學教育碩士班 99 Networks of coupled chaotic oscillators model many systems of interest in physics, electrical engineering, biology, laser systems, etc. In particular, complete chaotic synchronization, all oscillators acquiring identical chaotic behavior, has received much attention analytically. In 2007, global stability of synchronization in networks is studied by Juang et al. [Chaos, 17, 033111.11]. Their results apply to quite general connection topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. The lower bound on the coupling strength for synchronization is proportional to the inverse of the magnitude of the second largest eigenvalue λ2 of the coupling matrix. Therefore, the greater can greatly increase the applicable ranges of the coupling strengths. In 2002, Wei et al.[ Phys. Rev. Lett. 89, 284103.4] proposed a wavelet transform method to alter the connection topology. The wavelet transform method was reported that by modifying a tiny fraction of the wavelet subspace of a coupling matrix, the transverse stability of the synchronous manifold M of a coupled chaotic system could be dramatically enhanced. In other words, the wavelet transform method can greatly increase the applicable ranges of the coupling strengths and the number of oscillators for synchronization of networks of coupled chaotic systems. In this thesis, three kinds of circulant connection topologies are studied. First, the eigenvalues formulas for these coupling matrices are analytical found. Second, we sort the second largest eigenvalue by the eigenvalues formulas. Finally, we discuss how the wavelet transform method affects the synchronous phenomena in coupled chaotic systems for the coupling matrix with circulant connection topology. Chin-Lung Li 李金龍 2011 學位論文 ; thesis 19 zh-TW |
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碩士 === 國立新竹教育大學 === 人資處數學教育碩士班 === 99 === Networks of coupled chaotic oscillators model many systems of interest in physics, electrical engineering, biology, laser systems, etc. In particular, complete chaotic synchronization, all oscillators acquiring identical chaotic behavior, has received much attention analytically. In 2007, global stability of synchronization in networks is studied by Juang et al. [Chaos, 17, 033111.11]. Their results apply to quite general connection topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. The lower bound on the coupling strength for synchronization is proportional to the inverse of the magnitude of the second largest eigenvalue λ2 of the coupling matrix. Therefore, the greater can greatly increase the applicable ranges of the coupling strengths. In 2002, Wei et al.[ Phys. Rev. Lett. 89, 284103.4] proposed a wavelet transform method to alter the connection topology. The wavelet transform method was reported that by modifying a tiny fraction of the wavelet subspace of a coupling matrix, the transverse stability of the synchronous manifold M of a coupled chaotic system could be dramatically enhanced. In other words, the wavelet transform method can greatly increase the applicable ranges of the coupling strengths and the number of oscillators for synchronization of networks of coupled chaotic systems. In this thesis, three kinds of circulant connection topologies are studied. First, the eigenvalues formulas for these coupling matrices are analytical found. Second, we sort the second largest eigenvalue by the eigenvalues formulas. Finally, we discuss how the wavelet transform method affects the synchronous phenomena in coupled chaotic systems for the coupling matrix with circulant connection topology.
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Chin-Lung Li |
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Chin-Lung Li Chun-Kai Hsu 許竣凱 |
author |
Chun-Kai Hsu 許竣凱 |
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Chun-Kai Hsu 許竣凱 The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
author_sort |
Chun-Kai Hsu |
title |
The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
title_short |
The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
title_full |
The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
title_fullStr |
The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
title_full_unstemmed |
The Wavelet Transform Method for the Eigenvalues of an Asymmetrical Sparse Coupled Matrix and its Synchronous Applications |
title_sort |
wavelet transform method for the eigenvalues of an asymmetrical sparse coupled matrix and its synchronous applications |
publishDate |
2011 |
url |
http://ndltd.ncl.edu.tw/handle/73763588223852880290 |
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