随机常微分方程的均方lyapunov盆地构造

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2022-01-01 DOI:10.3934/jcd.2022024

Florian Rupp

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引用次数: 0

摘要

我们提出了一个简单的盆地搜索算法来确定一个合适的大的均方李雅普诺夫函数水平集，该水平集对应于随机常微分方程(RODE)的路径均衡解的线性化。噪声强度对RODEs解的行为与相应的确定性系统的相似程度起着至关重要的作用。在这方面，盆地搜索算法还允许在数值上估计噪声强度线性化均方渐近稳定性。

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Construction of mean-square Lyapunov-basins for random ordinary differential equations

We propose a straightforward basin search algorithm to determine a suitably large level set of the mean-square Lyapunov-function that corresponds to the linearization about an path-wise equilibrium solution of a random ordinary differential equation (RODE). Noise intensity plays a crucial role for how similar the behavior of solutions of RODEs is compared to the corresponding deterministic system. In this regards, the basin search algorithm also allows to numerically estimate up to which noise intensities linearized mean-square asymptotic stability remains.

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.