共查询到19条相似文献,搜索用时 125 毫秒
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将基于参数展开的同伦分析法(PE-HAM)进行了推广,使之适用于谐和激励与随机噪声联合作用下的强非线性随机动力系统. 通过构造合适的同伦映射,将对强非线性随机动力系统响应的求解转化为对一组线性随机微分方程的求解. 进一步研究了受到谐和与Gauss白噪声激励的强非线性Duffing振子,由PE-HAM得到了该系统的解过程和稳态概率密度的解析表达式. 数值模拟的结果说明了PE-HAM方法的精确性.
关键词:
PE-HAM方法
强非线性随机动力系统
稳态概率密度
解过程
随机激励 相似文献
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熵是热力学中表征物质状态的参量之一,是体系混乱程度的度量.一个信号的熵可以用来表示信号的复杂度. Duffing混沌系统从临界混沌状态向大尺度周期状态跃变的阈值是混沌系统分析的一个重要参数,它的求解方法是混沌理论目前亟待解决的问题之一.然而传统的实验分析法或者定量分析法存在一定的局限性.本文在研究中发现,系统处于混沌态和周期态时输出的多尺度熵值存在较大差异,且当系统进入周期态后多尺度熵值趋于平稳,基于这一现象结合遗传算法提出了基于多尺度熵的Duffing混沌系统阈值确定方法.利用该方法对正弦信号和方波信号的检测系统跃变阈值进行了计算,结果表明该方法快速准确且计算简单. 相似文献
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目前, 小波阈值去噪法、数字滤波法、傅里叶频域变换法等常用的微弱信号检测方法所能达到的最低检测信噪比为-10 dB, 而双向环形耦合Duffing振子能达到的最低检测信噪比为-20 dB. 但是, 现场检测时常常会出现更低信噪比的放电脉冲信号, 因此现有检测方法就很难满足信号检测的实际需求. 为了有效解决该难题, 研究了一种扩展型Duffing振子的微弱脉冲信号检测的新方法. 该方法的主要思想是使用广义时间尺度变换, 将Duffing振子模型变换为扩展型Duffing振子模型, 有效扩展了微弱信号的频率检测范围. 仿真结果表明, 扩展型Duffing振子不仅具有良好的噪声免疫特性, 而且能有效检测到信噪比低至-40 dB的局部放电微弱脉冲信号, 进一步扩展了现有Duffing振子微弱信号检测方法的检测范围和应用领域. 相似文献
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研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数 α 的改变也能诱导系统出现随机分岔现象.
关键词:
Lévy稳定噪声
Duffing-van der Pol振子
稳态概率密度函数
随机分岔 相似文献
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研究了Duffing单边约束系统在谐和与随机噪声联合激励下的响应问题. 用谐波平衡法和摄动法分析了系统在确定性谐和激励和随机激励联合作用下的响应,用随机平均法讨论了随机扰动项对系统响应的影响. 在一定条件下,当约束距离较大时对应于不同的初始条件,系统具有两个非碰撞的稳态响应;而当约束距离不大时,对应于不同的初始条件,系统也可以有两个不同的稳态响应,其中一个是发生碰撞的响应,而另外一个则不发生碰撞. 数值模拟表明该方法是有效的.
关键词:
Duffing单边约束系统
随机响应
谐波平衡法
摄动法 相似文献
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研究了级联双稳Duffing系统的随机共振特性, 证明级联双稳Duffing系统变尺度系数、阻尼比和级数等参数的适当调节, 不仅可实现大参数信号的级联随机共振, 而且可优化单级双稳Duffing系统的随机共振特征, 即参数调节的级联双稳Duffing系统能实现比单级双稳Duffing系统更好的随机共振输出. 此外, 级联双稳Duffing系统对方波信号具有良好的滤波整形作用, 可用于实现含噪方波信号的波形恢复.
关键词:
级联双稳Duffing系统
随机共振
变尺度
参数调节 相似文献
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A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It o stochastic differential equations. The Ito formula is then carried out to obtain the It o stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged Ito stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation. 相似文献
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A stochastic averaging procedure for a single-degree-of-freedom (SDOF) strongly nonlinear system with light damping modeled by a fractional derivative under Gaussian white noise excitations is developed by using the so-called generalized harmonic functions. The approximate stationary probability density and the largest Lyapunov exponent of the system are obtained from the averaged Itô stochastic differential equation of the system. It is shown that the approximate stationary solutions obtained by using the stochastic averaging procedure agree well with those from the numerical simulation of original systems. The effects of system parameters on the approxiamte stationary probability density and the largest Lyapunov exponent of the system are also discussed. 相似文献
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Stanisław Janeczko 《Letters in Mathematical Physics》1988,16(4):301-311
The topological type function for stationary probability density of stable stochastic dynamical systems is introduced. The corresponding bifurcation diagrams in the case of one dichotomic noise are derived. Examples encountered in physics and chemistry are given.The author was a visitor at the Department of Mathematics, Monash University, Australia, during part of the period when this paper was written. 相似文献
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The one-dimensional Sine-Gordon model where the field couples linearly to localized defects is studied. This model describes the phase fluctuations of one-dimensional charge density waves if amplitude fluctuations are neglected. For isolated defects the nonlinear stationarity conditions can be solved analytically. Given these stationary solutions the fluctuation spectrum consisting of a bound state and the scattering states and the relevant correlation functions can be computed exactly. The stationary states for a system of two defects are presented. The free energies as a function of the separation of the defects is computed for the absolutely stable states and for the local minima of the free energy function. This allows us to consider the interaction of the defects induced by the Sine-Gordon field. Finally we compute the order parameter correlation function for a random distribution of defects for small concentrationn. Devising a cumulant expansion the correlation function is found exactly in the first order inn. Our result contains the combined effect of the defects on the stationary states and on the phonon Green's function. It has applicability beyond the present context. 相似文献
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In this paper, stochastic behavior of FitzHugh–Nagumo neural system with two different kinds of time delays driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of the probability density approximation, the Fokker–Planck equation and the steady-state probability density function are derived. Then through the two-state theory, the analytical expression of the signal-to-noise ratio (SNR) is also obtained. Finally, the effects of time delays and noise auto-correlation times in nonlinear dynamical system on the stationary probability density and the SNR are discussed respectively. 相似文献
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B. Dybiec L. Schimansky-Geier 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):313-320
We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely
additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to
presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization
of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to
grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential
form. 相似文献