Techniques on Computations of Bifurcation of Sine-Gordon & Nonlinear Schrodinger ODE

• Main Authors: Chern, Jern Bin, 陳正斌
• Other Authors: Lee, Jong Eao
• Format: Others
• Language: en_US
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/68951811380789461950

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.