关于时滞微分方程的Floquet理论
On the Floquet Theory of Delay Differential Equations
摘要：
提出了一种分析方法来处理非线性时滞微分方程的时间周期参考态的不稳定性。为此，我们开始近似确定这样的参考状态，通过扩展庞加莱Lindstedt和Shohat展开，最初开发的常微分方程。然后，我们系统地阐述了一个时间周期参考状态的线性稳定性分析。这允许通过使用矩阵值连分数近似计算Floquet特征值和它们相应的特征解。
英文摘要：
We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.
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