Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE
碩士 === 國立交通大學 === 應用數學研究所 === 83 === In this thesis, based on the theory of continuation & local bifurcations, we develop numerical codes to sketch the bifurcation diagrams of the Sine-Gordon & nonlinear Schrodinger ODEs. From the b...
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ndltd-TW-083NCTU05070132015-10-13T12:53:40Z http://ndltd.ncl.edu.tw/handle/68951811380789461950 Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE Sine-Gordon與非線性Schrodinger對常微分方程之分岐現象的計算技巧 Chern, Jern Bin 陳正斌 碩士 國立交通大學 應用數學研究所 83 In this thesis, based on the theory of continuation & local bifurcations, we develop numerical codes to sketch the bifurcation diagrams of the Sine-Gordon & nonlinear Schrodinger ODEs. From the bifurcation diagrams, we realize the complicated qualitative behaviors of those ODEs. There exists bifurcation points such as turning points, pitchfork bifurcation points and Hopf bifurcation points. Also it indicates the existence of homoclinic orbits and strange attractors. The codes are shown to be correct by comparing the results with that previous results with that previous results done by [1],[10]. The codes, written in Mathematica, can be applied to general nonlinear ODEs with multi-parameters. Lee, Jong Eao 李榮耀 1995 學位論文 ; thesis 29 en_US |
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碩士 === 國立交通大學 === 應用數學研究所 === 83 === In this thesis, based on the theory of continuation & local
bifurcations, we develop numerical codes to sketch the
bifurcation diagrams of the Sine-Gordon & nonlinear Schrodinger
ODEs. From the bifurcation diagrams, we realize the complicated
qualitative behaviors of those ODEs. There exists bifurcation
points such as turning points, pitchfork bifurcation points and
Hopf bifurcation points. Also it indicates the existence of
homoclinic orbits and strange attractors. The codes are shown
to be correct by comparing the results with that previous
results with that previous results done by [1],[10]. The codes,
written in Mathematica, can be applied to general nonlinear
ODEs with multi-parameters.
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author2 |
Lee, Jong Eao |
author_facet |
Lee, Jong Eao Chern, Jern Bin 陳正斌 |
author |
Chern, Jern Bin 陳正斌 |
spellingShingle |
Chern, Jern Bin 陳正斌 Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
author_sort |
Chern, Jern Bin |
title |
Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
title_short |
Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
title_full |
Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
title_fullStr |
Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
title_full_unstemmed |
Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE |
title_sort |
techniques on computations of bifurcation of sine-gordon & nonlinear schrodinger ode |
publishDate |
1995 |
url |
http://ndltd.ncl.edu.tw/handle/68951811380789461950 |
work_keys_str_mv |
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