尋求不變集合的新演算法

Abstract

我們發展一個新的演算法以便較有效率地尋找動力系統中的類週期解，它能從一個 Hopf 分歧點開始平順地追蹤出整個類週期解群。我們以數個例子的測試來證明它的適用性，並對其中的 2-mode damped, driven sine-Gordon ODE 將有完整的分析。

We develop an algorithm to identify invariant curves efficiently. In dynamical systems, it helps do continuations of branches of quasi-periodic solutions smoothly in bifurcation diagrams. Several examples, especially for the 2-mode damped, driven sine-Gordon ODE, are demonstrated to provide the numerical evidence for the versatility of the algorithm.