标题： 动力系统不变性保持离散化方法 显示英文标题

标题： Invariance Preserving Discretization Methods of Dynamical Systems

摘要： 在本文中，我们考虑当将离散化方法应用于线性或非线性动力系统时，在集合上局部和统一不变性保持步长阈值。 对于前向或后向欧拉方法，当不变集为多面体、椭球或洛伦兹锥时，证明了局部和统一不变性保持步长阈值的存在性。 此外，我们还量化了后向欧拉方法在线性动力系统这些集合上的步长阈值。 最后，我们提出了关于一般离散化方法在一般凸集、紧集和适当锥上统一不变性保持步长阈值存在性的主要结果，适用于线性和非线性动力系统。 显示英文摘要

摘要： In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform invariance preserving steplength thresholds is proved when the invariant sets are polyhedra, ellipsoids, or Lorenz cones. Further, we also quantify the steplength thresholds of the backward Euler methods on these sets for linear dynamical systems. Finally, we present our main results on the existence of uniform invariance preserving steplength threshold of general discretization methods on general convex sets, compact sets, and proper cones both for linear and nonlinear dynamical systems.