Continuation-based Computation of Global Isochrons
Continuation-based Computation of Global Isochrons
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DOI：
10.1137/090777244
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
H. Osinga;J. Moehlis
中科院分区：
文献类型：
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作者：
H. Osinga;J. Moehlis
等时线是相空间的叶理，它将稳定周期轨道的相位概念扩展到该周期轨道的吸引盆。吸引盆中的每一点只位于一条等时线上，且同一条等时线上的两点收敛于具有相同相位的周期轨道。全局等时线，即扩展到整个吸引盆地而不仅仅是周期轨道附近的等时线，可以形成显著的叶理。例如，所有等时线的积累可以发生在相空间的任意小区域;这种积累的极限被称为无相集，它位于周期轨道吸引盆的边界上。由于整体等时线通常必须用数值近似，因此对于实际例子来说，这种复杂的几何形状通常难以实现。事实上，全球等时线的计算可能是具有挑战性的，特别是对于具有多个时间尺度的系统。我们提出了一种新的方法计算等时线…
Isochrons are foliations of phase space that extend the notion of phase of a stable periodic orbit to the basin of attraction of this periodic orbit. Each point in the basin of attraction lies on only one isochron, and two points on the same isochron converge to the periodic orbit with the same phase. Global isochrons, that is, isochrons extended into the full basin of attraction rather than just a neighborhood of the periodic orbit, can form remarkable foliations. For example, accumulations of all isochrons can occur in arbitrarily small regions of phase space; the limit of such an accumulation is called the phaseless set, which lies on the boundary of the basin of attraction of the periodic orbit. Since global isochrons must typically be approximated numerically, such complicated geometries are often difficult to realize for actual examples. Indeed, the computation of global isochrons can be challenging, particularly for systems with multiple time scales. We present a novel method for computing isochron...