当前位置: X-MOL 学术Differ. Integral Equ. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Noise-vanishing concentration and limit behaviors of periodic probability solutions
Differential and Integral Equations ( IF 1.4 ) Pub Date : 2020-05-16
Min Ji, Weiwei Qi, Zhongwei Shen, Yingfei Yi

The present paper is devoted to the investigation of noisy impacts on the dynamics of periodic ordinary differential equations (ODEs). To do so, we consider a family of stochastic differential equations resulting from a periodic ODE perturbed by small white noises, and study noise-vanishing behaviors of their “steady states” that are characterized by periodic probability solutions of the associated Fokker-Plank equations. By establishing noise-vanishing concentration estimates of periodic probability solutions, we prove that any limit measure of periodic probability solutions must be a periodically invariant measure of the ODE and that the global periodic attractor of a dissipative ODE is stable under general small noise perturbations. For local periodic attractors (resp. local periodic repellers), small noises are constructed to stabilize (resp. de-stabilize) them. Our study provides an elementary step towards the understanding of stochastic stability of periodic ODEs.

中文翻译:

消除噪声的集中和周期概率解的极限行为

本文致力于研究噪声对周期常微分方程(ODE)动力学的影响。为此,我们考虑由周期性ODE引起的一系列随机微分方程,这些ODE受小白噪声干扰,并研究其“稳态”的消失特性,这些行为的特征在于相关Fokker-Plank方程的周期性概率解。通过建立周期概率解的消失的集中估计,我们证明周期概率解的任何极限度量都必须是ODE的周期不变度量,并且耗散ODE的全局周期吸引子在一般的小噪声扰动下是稳定的。对于局部周期性吸引器(分别是局部周期性排斥器),会产生较小的噪音以使其稳定(重复)。破坏稳定)。我们的研究为理解周期性ODE的随机稳定性提供了基本步骤。
更新日期:2020-05-16
down
wechat
bug