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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Determining the self-rotation number following a Naimark-Sacker bifurcation in the periodically forced Taylor-Couette flow
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Determining the self-rotation number following a Naimark-Sacker bifurcation in the periodically forced Taylor-Couette flow

机译：确定周期性强迫泰勒-柯伊特流中奈马克-萨克分叉后的自转数

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摘要

Systems which admit waves via Hopf bifurcations and even systems that do not undergo a Hopf bifurcation but which support weakly damped waves may, when parametrically excited, respond quasiperiodically. The bifurcations are from a limit cycle (the time-periodic basic flow) to a torus, i.e. Naimark-Sacker bifurcations. Floquet analysis detects such bifurcations, but does not unambiguously determine the second frequency following such a bifurcation. Here we present a technique to unambiguously determine the frequencies of such quasiperiodic flows using only results from Floquet theory and the uniqueness of the self-rotation number (the generalization of the rotation number for continuous systems). The robustness of the technique is illustrated in a parametrically excited Taylor-Couette flow, even in cases where the bifurcating solutions are subject to catastrophic jumps in their spatial/temporal structure.
机译：通过参数霍普夫分叉允许波进入的系统，甚至不经历霍夫夫分叉但支持弱阻尼波的系统，在被参量激发时，也可能是准周期性的。分叉是从极限周期（时间周期基本流）到圆环，即Naimark-Sacker分叉。浮球分析检测到这样的分叉，但是不能明确地确定这样的分叉之后的第二频率。在这里，我们提出一种仅使用Floquet理论的结果和自转数的唯一性（连续系统的转数的一般化）即可明确确定此类准周期流的频率的技术。即使在分叉解在其空间/时间结构中遭受灾难性跳跃的情况下，该技术的鲁棒性也在参量激发的Taylor-Couette流中得以说明。

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