Mathematical analysis of the Wiener processes with time-delayed feedback

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

引用次数: 0

Abstract

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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具有延时反馈的维纳过程的数学分析

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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