Abstract

The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and Lévy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the neighborhood of one of the limit cycles influences the coherence of the dynamics on the time scale of the oscillations. The autocorrelation function, the power spectral density and the signal-to-noise-ratio used in this analysis are shown to be maximized for an appropriate choice of the noise intensity. In particular, a proper adjustment of the Lévy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the resonance, as examined using standard measures, seems to occur also in the presence of nonstandard noise. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the Lévy noise has not a notable impact on the resonant effect.

Graphical abstract

中文翻译：

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Lévy噪声能否在双节律性范德波尔系统中引起相干和随机共振？

摘要

对由周期激励和Lévy噪声驱动的双节律性修改型van der Pol型振荡器的分析表明，可能发生相干共振和随机共振。极限周期之一附近的谐波激励频率会影响动力学在时间尺度上的相干性。的自相关函数中，功率谱密度和在该分析中使用的信号 - 噪声比被示为被最大化为噪声强度的一个合适的选择。特别是，对Lévy噪声强度的适当调整会增强系统的输出功率谱，即会促进随机共振。因此，使用标准方法检查的共振似乎也出现在非标准噪声的情况下。

图形概要