Parametric Resonance of the Non-Markovian Oscillator

IF 0.8 4区 地球科学 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC Radiophysics and Quantum Electronics Pub Date : 2024-02-09 DOI:10.1007/s11141-024-10294-y
O. L. Sirotkin, N. A. Koplevatsky
{"title":"Parametric Resonance of the Non-Markovian Oscillator","authors":"O. L. Sirotkin,&nbsp;N. A. Koplevatsky","doi":"10.1007/s11141-024-10294-y","DOIUrl":null,"url":null,"abstract":"<p>We develop differential equations for the probability density of the phase coordinates of the dynamic systems with parametric fluctuations in the form of the non-Markovian dichotomic noise, which has arbitrary lifetime distribution functions in the states ±1. As an example, we calculate the first moment of the phase coordinate of the linear oscillator, whose perturbed motion is described by the stochastic analogue of the Mathieu—Hill equation. These calculations aim at demonstrating the fact that in the case of linear dynamic systems, the non-Markovian parametric fluctuations having hidden periodicity are capable of inducing the states absent in the deterministic regime without periodic coefficients. The problem is solved by the method of supplementary variables, which transforms the non-Markovian dichotomic noise to the Markovian noise. It is shown that the amplitude oscillations, which are typical of the parametric resonance are present, when the structure of the dichotomic noise is described by the lifetime distribution function in the states ±1 in the form of the sum of weighted Erlang distribution exponents of the various order and a constant value of +1. The delta-correlated and Gaussian properties of the studied processes are not used. The calculations are performed within the framework of simple differential equations without involving integral operators and the Novikov—Furutsu—Donsker theorem.</p>","PeriodicalId":748,"journal":{"name":"Radiophysics and Quantum Electronics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Radiophysics and Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11141-024-10294-y","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0

Abstract

We develop differential equations for the probability density of the phase coordinates of the dynamic systems with parametric fluctuations in the form of the non-Markovian dichotomic noise, which has arbitrary lifetime distribution functions in the states ±1. As an example, we calculate the first moment of the phase coordinate of the linear oscillator, whose perturbed motion is described by the stochastic analogue of the Mathieu—Hill equation. These calculations aim at demonstrating the fact that in the case of linear dynamic systems, the non-Markovian parametric fluctuations having hidden periodicity are capable of inducing the states absent in the deterministic regime without periodic coefficients. The problem is solved by the method of supplementary variables, which transforms the non-Markovian dichotomic noise to the Markovian noise. It is shown that the amplitude oscillations, which are typical of the parametric resonance are present, when the structure of the dichotomic noise is described by the lifetime distribution function in the states ±1 in the form of the sum of weighted Erlang distribution exponents of the various order and a constant value of +1. The delta-correlated and Gaussian properties of the studied processes are not used. The calculations are performed within the framework of simple differential equations without involving integral operators and the Novikov—Furutsu—Donsker theorem.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
非马尔可夫振荡器的参数共振
例如,我们计算了线性振荡器相位坐标的第一矩,该振荡器的扰动运动由马修-希尔方程的随机类似方程描述。这些计算旨在证明这样一个事实,即在线性动态系统中,具有隐含周期性的非马尔可夫参数波动能够诱导出在没有周期性系数的确定性系统中不存在的状态。这个问题是通过补充变量法解决的,该方法将非马尔可夫二分噪声转化为马尔可夫噪声。结果表明,当二分噪声的结构是由±1状态下的寿命分布函数以各阶加权厄朗分布指数之和和常数+1的形式描述时,会出现参量共振的典型振幅振荡。没有使用所研究过程的德尔塔相关和高斯特性。计算是在简单微分方程的框架内进行的,不涉及积分算子和诺维科夫-富留津-唐斯克定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Radiophysics and Quantum Electronics
Radiophysics and Quantum Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED
CiteScore
1.10
自引率
12.50%
发文量
60
审稿时长
6-12 weeks
期刊介绍: Radiophysics and Quantum Electronics contains the most recent and best Russian research on topics such as: Radio astronomy; Plasma astrophysics; Ionospheric, atmospheric and oceanic physics; Radiowave propagation; Quantum radiophysics; Pphysics of oscillations and waves; Physics of plasmas; Statistical radiophysics; Electrodynamics; Vacuum and plasma electronics; Acoustics; Solid-state electronics. Radiophysics and Quantum Electronics is a translation of the Russian journal Izvestiya VUZ. Radiofizika, published by the Radiophysical Research Institute and N.I. Lobachevsky State University at Nizhnii Novgorod, Russia. The Russian volume-year is published in English beginning in April. All articles are peer-reviewed.
期刊最新文献
Scalable Quantum Processor Based on Superconducting Fluxonium Qubits Integrated Circuits for Quantum Machine Learning Based on Superconducting Artificial Atoms and Methods of Their Control Waveguide Integrated Superconducting Single-Photon Detector For Photonic And Ion Quantum Processors And Neuromorphic Computing The Influence of Cyclic Deformation on Elastic and Acoustic Properties of Chromium-Nickel Steels Development of a Microwave Diagnostic Method for Measurements of the Free-Surface Velocity in the Plane-Wave Experiment
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1