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ID 114910
著者
津元, 国親 Osaka University
川上, 博 Japan Science and Technology Agency 徳島大学 教育研究者総覧
キーワード
nonlinear dynamical system
bifurcation
boundary value problem
variational equation
Newton's method
資料タイプ
学術雑誌論文
抄録
In this paper, we explain how to compute bifurcation parameter values of periodic solutions for non-autonomous nonlinear differential equations. Although various approaches and tools are available for solving this problem nowadays, we have devised a very simple method composed only of basic computational algorithms appearing in textbooks for beginner's, i.e., Newton's method and the Runge-Kutta method. We formulate the bifurcation problem as a boundary value problem and use Newton's method as a solver consistently. All derivatives required in each iteration are obtained by solving variational equations about the state and the parameter. Thanks to the quadratic convergence ability of Newton's method, accurate results can be quickly and effectively obtained without using any sophisticated mathematical library or software. If a discontinuous periodic force is applied to the system, we can use the same strategy to solve the bifurcation problem. The key point of this method is deriving a differentiable composite map from the various information about the problem such as the location of sections, the periodicity, the Poincaré mapping, etc.
掲載誌名
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
出版者
The Institute of Electronics, Information and Communication Engineers
3
4
開始ページ
458
終了ページ
476
発行日
2012-10-01
権利情報
© IEICE 2012
EDB ID
出版社版DOI
出版社版URL
フルテキストファイル
言語
eng
著者版フラグ
出版社版
部局
情報センター
医学系
理工学系