Effects of the Low Frequencies of Noise on On–Off Intermittency

Effects of the Low Frequencies of Noise on On–Off Intermittency
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低频噪声对开关间歇性的影响

DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
F. Pétrélis
F. Pétrélis
中科院分区：
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文献类型：
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作者：
S. Aumaitre;K. Mallick;F. Pétrélis

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受乘性噪声影响的分叉系统可以表现出接近不稳定阈值的开关不稳定性。对于一个正则系统，我们讨论了这种不稳定性对噪声功率谱密度（PSD）的依赖性。我们的研究是基于不稳定变量的概率密度函数（PDF）的计算。我们推导出一些特定类型的噪声的分析结果，并解释它们的开-关不相干性的框架。此外，我们进行累积展开（N。G.货车坎彭，24，171（1976）。）对于具有任意功率谱密度的随机噪声，我们表明，间歇制度是由从阈值的偏离和零频率处的噪声的PSD值之间的比率控制。我们的研究结果与两种随机扰动的数值模拟结果一致：高斯色噪声和混沌变量的确定性波动。这项研究的扩展到另一个，更复杂的系统，并讨论了潜在的机制。
A bifurcating system subject to multiplicative noise can exhibit on–off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion (N. G. van Kampen, 24, 171 (1976).) for a random noise with arbitrary power spectrum density and we show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.