具有延时反馈的维纳过程的数学分析

IF 1.4 4区物理与天体物理 Q4 MATERIALS SCIENCE, MULTIDISCIPLINARY AIP Advances Pub Date : 2024-09-19 DOI:10.1063/5.0209241

Miki U. Kobayashi, Kohta Takehara, Hiroyasu Ando, Michio Yamada

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引用次数: 0

摘要

众所周知，时间延迟通常会导致系统不稳定。然而，从数值上可以观察到，具有时间延迟反馈的维纳过程的扩散系数会随着时间延迟τ的增加而减小。特别是，数值模拟已经证实了形式为（11+τ）2 的扩散系数的衰减[Ando 等人，Phys.在本文中，我们通过拉普拉斯变换和随机微分方程的动态系统方法，提出了 (11+τ)2 关系的两种分析推导。

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Mathematical analysis of the Wiener processes with time-delayed feedback

It is known that time delays generally make a system unstable. However, it is numerically observed that the diffusion coefficients of the Wiener processes with time-delayed feedback decrease while increasing the time delay τ. In particular, the decay of the diffusion coefficients with the form (11+τ)2 has been confirmed by numerical simulations [Ando et al., Phys. Rev. E 96, 012148 (2017)]. In this paper, we present two analytical derivations for the relation (11+τ)2 by dynamical system approaches using the Laplace transform and stochastic differential equations.

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来源期刊

AIP Advances NANOSCIENCE & NANOTECHNOLOGY-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

2.80

自引率

6.20%

发文量

1233

审稿时长

2-4 weeks

期刊介绍： AIP Advances is an open access journal publishing in all areas of physical sciences—applied, theoretical, and experimental. All published articles are freely available to read, download, and share. The journal prides itself on the belief that all good science is important and relevant. Our inclusive scope and publication standards make it an essential outlet for scientists in the physical sciences. AIP Advances is a community-based journal, with a fast production cycle. The quick publication process and open-access model allows us to quickly distribute new scientific concepts. Our Editors, assisted by peer review, determine whether a manuscript is technically correct and original. After publication, the readership evaluates whether a manuscript is timely, relevant, or significant.