Geometry of inertial manifolds probed via a Lyapunov projection method.
Geometry of inertial manifolds probed via a Lyapunov projection method.
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DOI：
10.1103/physrevlett.108.154101
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发表时间：
2011-12
影响因子：
8.6
通讯作者：
Hong-liu Yang;G. Radons
中科院分区：
文献类型：
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作者：
Hong-liu Yang;G. Radons
提出了一种确定耗散扩展动力系统惯性流形的维数和状态空间几何形状的方法。它的工作原理是将参考状态和循环状态之间的向量差投影到由李亚普诺夫向量跨越的局部线性子空间上。一旦基向量的数量增加到超出惯性流形维数，投影误差就会发生急剧的特征转变。由于该方法可以使用标准正交李亚普诺夫向量来应用，因此它提供了一种可能的方法来确定实验惯性流形及其几何特征。
A method for determining the dimension and state space geometry of inertial manifolds of dissipative extended dynamical systems is presented. It works by projecting vector differences between reference states and recurrent states onto local linear subspaces spanned by the Lyapunov vectors. A sharp characteristic transition of the projection error occurs as soon as the number of basis vectors is increased beyond the inertial manifold dimension. Since the method can be applied using standard orthogonal Lyapunov vectors, it provides a possible way to also determine experimentally inertial manifolds and their geometric characteristics.