Degenerate isostable reduction for fixed-point and limit-cycle attractors with defective linearizations
Degenerate isostable reduction for fixed-point and limit-cycle attractors with defective linearizations
复制标题
具有缺陷线性化的定点和极限环吸引子的简并等稳态约简
DOI：
10.1103/physreve.103.022211
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Wilson, Dan
中科院分区：
文献类型：
--
作者：
Wilson, Dan
等稳坐标为理解具有稳定吸引子的动力系统的瞬态行为提供了一个方便的框架。这些等稳坐标通常用来描述库普曼算子的衰减最慢的特征函数；忽略快速衰减的库普曼特征函数可以得到降阶模型。现有的工作主要集中在非简并等稳坐标上，即与具有相同代数和几何多重性的特征值相关的等稳坐标。目前的等稳约简方法不能用于表征与缺陷特征值相关的衰减。在这项工作中，提出了一个退化的等稳框架，用于当特征值是缺陷的。这些退化等稳坐标是在各种降阶建模框架的背景下研究的，这些框架保留了许多标准（非退化）等稳约简建模策略的重要性质。需要使用退化等稳坐标的降阶建模示例与昼夜生理学和非线性流体流动相关。
Isostable coordinates provide a convenient framework for understanding the transient behavior of dynamical systems with stable attractors. These isostable coordinates are often used to characterize the slowest decaying eigenfunctions of the Koopman operator; by neglecting the rapidly decaying Koopman eigenfunctions a reduced order model can be obtained. Existing work has focused primarily on nondegenerate isostable coordinates, that is, isostable coordinates that are associated with eigenvalues that have identical algebraic and geometric multiplicities. Current isostable reduction methods cannot be applied to characterize the decay associated with a defective eigenvalue. In this work, a degenerate isostable framework is proposed for use when eigenvalues are defective. These degenerate isostable coordinates are investigated in the context of various reduced order modeling frameworks that retain many of the important properties of standard (nondegenerate) isostable reduced modeling strategies. Reduced order modeling examples that require the use of degenerate isostable coordinates are presented with relevance to both circadian physiology and nonlinear fluid flows.