Trajectory-free approximation of phase space structures using the trajectory divergence rate
Trajectory-free approximation of phase space structures using the trajectory divergence rate
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DOI：
10.1007/s11071-019-04814-z
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发表时间：
2017-05
影响因子：
5.6
通讯作者：
Gary K. Nave;Peter J. Nolan;S. Ross
中科院分区：
文献类型：
--
作者：
Gary K. Nave;Peter J. Nolan;S. Ross
本文引入了轨道发散率，这是一个局部给出相邻轨道瞬时吸引或排斥的标量场。这个标量场可以用来寻找高度吸引或排斥的不变流形，如慢流形，以快速近似双曲拉格朗日相干结构，或提供不变流形的局部稳定性。这项工作提出了推导的轨迹发散率和相关的轨迹发散比为二维系统，研究其属性，显示其应用程序的几个例子系统，并提出了他们的扩展到更高的维度。
This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant manifolds, such as slow manifolds, to rapidly approximate hyperbolic Lagrangian coherent structures, or to provide the local stability of invariant manifolds. This work presents the derivation of the trajectory divergence rate and the related trajectory divergence ratio for two-dimensional systems, investigates their properties, shows their application to several example systems, and presents their extension to higher dimensions.