共查询到15条相似文献,搜索用时 64 毫秒
1.
以含分数阶微分项的van der Pol振子为对象,研究其超谐共振时的动力学特性.首先,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,研究了分数阶微分项的系数和阶次以等效线性阻尼和等效线性刚度的形式对系统动力学特性的影响.随后,建立了超谐共振时定常解的幅频曲线的解析表达式,得到了超谐共振周期响应的稳定性判断准则并提出等效非线性阻尼和非线性稳定性条件参数的概念.最后,通过数值仿真比较了分数阶与整数阶系统的幅频曲线,分析了分数阶微分项的系数和阶次对响应幅值、幅频曲线以及系统稳定性的影响. 相似文献
2.
研究了一类随机van der Pol 系统的Hopf分岔行为.首先根据Hilbert空间的正交展开理论,含有随机参数的van der Pol系统被约化为等价确定性系统,然后利用确定性分岔理论分析了等价系统的Hopf分岔,得出了随机van der Pol 系统的Hopf 分岔临界点,探究了随机参数对系统Hopf分岔的影响.最后利用数值模拟验证了理论分析结果.
关键词:
随机van der Pol系统
Hopf分岔
正交多项式逼近 相似文献
3.
利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机van der Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法.
关键词:
非光滑动力系统
随机 van der Pol系统
擦边分岔
双边约束 相似文献
4.
应用 Chebyshev 多项式逼近法研究了谐和激励作用下具有随机参数的随机van der Pol系统 的倍周期分岔现象.随机系统首先被转化成等价的确定性系统,然后通过数值方法求得响应 ,借此探索了随机van der Pol系统丰富的随机倍周期分岔现象.数值模拟显示随机van der Pol 系统存在与确定性系统极为相似的倍周期分岔行为,但受随机因素的影响,又有与之不 同之处.数值结果表明,Chebyshev 多项式逼近是研究非线性系统动力学问题的一种新的有 效方法.
关键词:
Chebyshev 多项式
随机van der Pol 系统
倍周期分岔 相似文献
5.
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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8.
讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象,并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法,将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统,使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题,继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明,随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道,但是在随机参数及其强度的影响下也呈现出一些特点. 相似文献
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10.
讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统,然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为,同时指出,随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法.
关键词:
Chebyshev多项式
随机Duffing-van der Pol系统
倍周期分岔 相似文献
11.
This paper applies washout filter technology to amplitude
control of limit cycles emerging from Hopf bifurcation of the van der
Pol--Duffing system. The controlling parameters for the appearance
of Hopf bifurcation are given by the Routh--Hurwitz criteria.
Noticeably, numerical simulation indicates that the controllers
control the amplitude of limit cycles not only of the weakly nonlinear van
der Pol--Duffing system but also of the strongly nonlinear van der
Pol--Duffing system. In particular, the emergence of Hopf bifurcation
can be controlled by a suitable choice of controlling parameters.
Gain-amplitude curves of controlled systems are also drawn. 相似文献
12.
Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling 下载免费PDF全文
In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays. 相似文献
13.
Renato Spigler 《Journal of statistical physics》1985,41(1-2):175-200
Astochastic model for some class ofnonlinear oscillators, which includes a van der Pol-type oscillator with random parameters, is analyzed in thediffusion limit. That is, small random fluctuations and long time are considered, while the nonlinearity is also assumed to be small. We show that there existstationary distributions, independent of the phase of the oscillator, a result proved earlier by R. L. Stratonovich assuming the random perturbations of the frequency to be delta correlated. The time behavior of the moments of the displacement of the oscillator from its rest position is also investigated and the results are compared with the corresponding ones for the linear random oscillator. A numerical study is also performed for the first two moments and plots are given.on leave from the University of Padua, Italy. 相似文献
14.
Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation 下载免费PDF全文
This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. 相似文献
15.
S Rajasekar 《Pramana》1993,41(4):295-309
This paper investigates the possibility of controlling horseshoe and asymptotic chaos in the Duffing-van der Pol oscillator
by both periodic parametric perturbation and addition of second periodic force. Using Melnikov method the effect of weak perturbations
on horseshoe chaos is studied. Parametric regimes where suppression of horseshoe occurs are predicted. Analytical predictions
are demonstrated through direct numerical simulations. Starting from asymptotic chaos we show the recovery of periodic motion
for a range of values of amplitude and frequency of the periodic perturbations. Interestingly, suppression of chaos is found
in the parametric regimes where the Melnikov function does not change sign. 相似文献