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The bifurcation of noisy bistable Duffing oscillator''s moment equations and stochastic resonance
含噪双稳杜芬振子矩方程的分岔与随机共振

Zhang Guangjun,Xu Jianxue,Yao Hong,
张广军
,徐健学,姚宏

力学学报 , 2006,
Abstract: In this paper,the relationship between the bifurcation of noisy bistable Duffing oscillator's moment equations and stochastic resonance of this system is studied.According to the relationship, the mechanism of stochastic resonance of the bistable Duffing oscillator is revealed from another viewpoint. First, the moment equations of the bistable Duffing oscillator in the presence of Gaussian distributed white noise and weak periodic signal are obtained on the basis of Ito equation.Second,the bifurcation behavior of its moment equations with noise intensity as their bifurcation parameter is analyzed.Third,the relationship between stochastic resonance of the bistable Duffing oscillator and the behavior of bifurcation of the moment equations is studied quantitatively. Finally,the mechanism of stochastic resonance of the bistable Duffing oscillator is presented from another viewpoint, that is, the transfer of the energy distribution of the first moment of the original system response occurs because of occurrence of bifurcation of the moment equations with noise intensity bifurcation parameter, and the transfer makes the energy of system response concentrate in the frequency component whose frequency is equal to that of input, then the weak signal is amplified and stochastic resonance occurs.
含噪双稳杜芬振子矩方程的分岔与随机共振  [PDF]
张广军,徐健学,姚宏
力学学报 , 2006, DOI: 10.6052/0459-1879-2006-2-2004-414
Abstract: 研究了含噪声的双稳杜芬振子矩方程的分岔与随机共振的关系,并根据它们的关系,从另一个角度揭示了随机共振发生的机制.首先在It?方程的基础上,导出了双稳杜芬振子在白噪声和弱周期信号作用下的矩方程,其次以噪声强度为分岔参数分析了矩方程的分岔特性,再次分析了矩方程的分岔与双稳杜芬振子随机共振之间的关系,最后根据该对应关系从另一种观点提出了双稳杜芬振子随机共振的机制,该机制是由于以噪声强度为分岔参数的矩方程发生了分岔,而分岔使得原系统响应均值的能量分布发生了转移,使能量向频率等于输入信号频率的分量处集中,使得弱信号得到了放大,随机共振发生了.
双稳杜芬振子的随机共振及其动力学机制  [PDF]
康艳梅,徐健学,谢勇
力学学报 , 2004, DOI: 10.6052/0459-1879-2004-2-2003-293
Abstract: 把矩方法应用于高斯白噪声和弱周期信号驱动的双稳杜芬振子,发现矩方法的收敛快慢与阻尼系数的大小有关,即在固定非线性参数的前提下,阻尼系数越大,收敛速度越快.在阻尼系数较大的情形,对于不同频率的弱周期输入信号,系统输出功率谱增益因子的演化随噪声强度呈单峰或双峰结构,亦即对于不同的激励频率,系统可表现出单峰或者重峰随机共振结构.为了解释这些共振结构,通过考察由波动谱密度定义的非零频率峰对噪声强度依赖性,发现重峰随机共振的发生在于噪声一方面抑制了井内运动,另一方面诱发了势垒上振动.研究结果为已有结论的修正,在统计力学等方面具有显著意义.
Study on Linearization Criterion and Vibration Mechanism based on Duffing Systems
基于杜芬系统的线性化准则与振动机理研究

LI Da-wang,XING Feng,WANG Jiay-uan,
李大望
,邢锋,王家远

系统工程理论与实践 , 2007,
Abstract: Based on the two assessment indexes of the equivalent error rate and entropy error rate,the predict precision of the analytic linearization solutions of the steady-state response distribution of Duffing systems to Gaussian white noises is contrastively analyzed,abided by the two equivalent criterions of response moment limited and minimizing the mean square of equation difference,respectively; the relativity between the systemic parameters and excitation intensity,and their synthetical influence on systemic vibrations are discussed.The results show that the predict precision of the linearization solutions is controlled by the principle of maximum entropy;the basic attribute of linearization solutions is located by the criterion of minimizing the mean square of equation difference,and its forecast precision may be improved by use of known moment information;the assessment conclusions corresponding to the two indexes above-mentioned have consistency;the influences of the systemic parameters and excitation intensity on response distributions can be synthetically expressed by the relative hardening stiffness coefficient.
Duffing振子强迫振动的混沌特性仿真分析  [PDF]
黄胜伟
力学与实践 , 2002, DOI: 10.6052/1000-0992-2000-424
Abstract: 根据Duffing振子强迫振动系统的数学模型,编制该动力系统的计算机仿真软件.通过对Duffing方程实例仿真分析,探讨该类方程出现混沌的各参数之间的关系,可全面分析混沌动力系统特性.
分数阶Duffing振子的超谐共振  [PDF]
申永军,杨绍普,邢海军
力学学报 , 2012, DOI: 10.6052/0459-1879-11-378
Abstract: 研究了含分数阶微分项的Duffing振子的超谐共振,通过平均法得到了系统的一阶近似解.提出了超谐共振时等效线性阻尼和等效线性刚度的概念,分析了分数阶微分项的系数和阶次对等效线性阻尼和等效线性刚度的影响.建立了超谐共振解的幅频曲线的解析表达式和稳定性判断准则,对分数阶Duffing振子与传统整数阶Duffing振子的超谐共振解进行了比较.最后通过数值仿真研究了分数阶微分项的参数对超谐共振幅频曲线的影响.
基于扩展型Duffing振子的高精度测频方法  [PDF]
罗志坤,曾喆昭
电力系统自动化 , 2015, DOI: 10.7500/AEPS20140728013
Abstract: 针对Duffing振子在信号检测方面存在的局限性,提出了基于扩展型Duffing振子的电力系统基波频率检测新方法。所提的扩展型Duffing振子的临界混沌幅值不会随振子激励频率和采样频率的显著变化而变化。对任意激励频率和采样频率,其临界混沌幅值几乎保持恒定,有效避免了传统Duffing振子只能检测低频信号的局限性。其检测原理是使用特定频率的周期扰动使扩展型Duffing振子产生共振,从而实现基波频率检测。研究结果表明,扩展型Duffing振子具有良好的噪声免疫特性,在一组确定的参数条件下即可实现电力系统基波频率的高精度检测。
基于Duffing振子大周期态相轨迹的频率测量方法  [PDF]
刘海波,吴德伟,卢虎,王永庆,蒋文婷
电子学报 , 2013, DOI: 10.3969/j.issn.0372-2112.2013.10.022
Abstract: 对Duffing振子大周期态相轨迹特性进行了研究,提出了一种利用Duffing振子大周期相轨迹运动实现频率测量的方法.仿真结果表明,该方法的检测信噪比下限要高于现有的基于强参考模式的检测方法,但该方法不存在检测盲区问题,在单振子频率覆盖方面也有了大幅提高,极大降低了检测系统的设计难度,而且单振子即可实现对chirp信号的检测,拓展了Duffing振子检测技术的应用.
基于经验模态分解和Duffing振子的轴承故障诊断  [PDF]
关贞珍,郑海起,杨云涛,王彦刚
农业机械学报 , 2010,
Abstract: 针对齿轮箱轴承振动信号故障信息容易被噪声淹没,且具有非线性、非平稳特性的问题,提出了基于经验模态分解(EMD)和Duffing振子的轴承故障诊断方法。首先对原始振动信号进行经验模态分解,找到包含轴承故障信息的固有模态函数(IMF),然后利用Duffing振子的分岔图找到混沌振子相轨迹发生变化的内部激励力分界值,并将Duffing振子的内部激励力频率设定为轴承故障特征频率,最后从混沌振子输出相轨迹的变化来检测齿轮箱轴承故障信息。实验结果表明,基于EMD和Duffing振子的故障诊断方法能够检测轴承故障信息。
Duffing混沌振子微弱信号检测方法研究  [PDF]
高振斌,刘晓哲,郑娜
重庆邮电大学学报(自然科学版) , 2013,
Abstract: 研究了采用Duffing混沌振子检测微弱正弦信号频率的可行性并分析了检测性能,提出了利用混沌振子输出方差极值对来检测微弱正弦信号的方法。首先根据混沌振子周期策动力与待测信号频率相等时,系统输出方差值最大这一性质,研究了采样频率对检测结果的影响。实验结果表明,通过增大采样频率并增加数据序列长度,在信噪比-45dB时可以检测出信号。然后,将此性质应用于与周期策动力有随机相位差的正弦信号检测中,发现在二者频率接近或相等时,系统输出方差值发生跳变,出现一个极大值和一个极小值对,通过这一新的特性可以检测出与激励信号有相位差的信号频率。最后将此方法成功应用于调幅波的频率检测中。
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