Nonautonomous finite-time dynamics
Nonautonomous finite-time dynamics
复制标题
非自主有限时间动力学
DOI：
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复制
发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Siegmund
中科院分区：
文献类型：
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作者：
A. Berger;Doan Thai Son;S. Siegmund
有限时间区间上的非自治微分方程
在包含以下内容的应用中发挥着越来越重要的作用
时变矢量场，例如观测或预测的速度
在气象学或海洋学领域，
从一个紧凑的区间乘以t。虽然经典动力学
系统方法经常研究解的行为，如$t\to
\pm\infty $，动态分区（最初称为EPH
划分）的目的是描述和分类的有限时间
性能.我们讨论了动力学的基本性质
分区，并表明它局部逼近的非线性
性能.我们还提供了一个实用的算法
并将其应用于非线性三维
example.
Nonautonomous differential equations on finite-time intervals play
an increasingly important role in applications that incorporate
time-varying vector fields, e.g. observed or forecasted velocity
fields in meteorology or oceanography which are known only for
times $t$ from a compact interval. While classical dynamical
systems methods often study the behaviour of solutions as $t \to
\pm\infty$, the dynamic partition (originally called the EPH
partition) aims at describing and classifying the finite-time
behaviour. We discuss fundamental properties of the dynamic
partition and show that it locally approximates the nonlinear
behaviour. We also provide an algorithm for practical computations
with dynamic partitions and apply it to a nonlinear 3-dimensional
example.