Noise-Induced Stabilization of Perturbed Hamiltonian Systems
Noise-Induced Stabilization of Perturbed Hamiltonian Systems
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DOI：
10.1080/00029890.2019.1586502
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Tiffany N. Kolba;A. Coniglio;S. Sparks;Daniel Weithers
中科院分区：
文献类型：
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作者：
Tiffany N. Kolba;A. Coniglio;S. Sparks;Daniel Weithers
噪声诱导镇定是指在不稳定的常微分方程系统中加入随机性，使系统稳定的现象。稳定性定义为全局随机有界性，Hamilton系统永远不能通过添加空间常数的噪声来稳定。在这篇文章中，我们研究如何确定性扰动一类不稳定的哈密顿系统，以这样一种方式，保持定性行为，但使系统表现出噪声诱导稳定。
Abstract Noise-induced stabilization is the phenomenon in which the addition of randomness to an unstable system of ordinary differential equations results in a stable system of stochastic differential equations. With stability defined as global stochastic boundedness, Hamiltonian systems can never be stabilized by the addition of noise that is constant in space. In this article, we investigate how to deterministically perturb a class of unstable Hamiltonian systems in such a way that the qualitative behavior is preserved, but that enables the systems to exhibit noise-induced stabilization.