Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle.
Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle.
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DOI：
10.1063/1.2779852
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发表时间：
2008-03
期刊：
影响因子：
2.9
通讯作者：
C. Muratov;E. Vanden-Eijnden
中科院分区：
文献类型：
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作者：
C. Muratov;E. Vanden-Eijnden
对小高斯白噪声对经历超临界 Hopf 分岔的弛豫振荡器的影响进行了详细的渐近研究。分析揭示了复杂的随机分岔，导致在不同噪声幅度水平下出现多种噪声驱动的混合模式振荡。在强时间尺度分离的限制下，确定了噪声幅度的五种不同的缩放机制。随着噪声幅度的减小，系统的动力学从自感随机共振引起的极限环到相干共振极限环，然后到突发弛豫振荡，然后是罕见的几个弛豫周期簇（尖峰），最后到具有零星单尖峰的小幅度振荡（或稳定不动点）。这些情景得到了数值模拟的证实。
A detailed asymptotic study of the effect of small Gaussian white noise on a relaxation oscillator undergoing a supercritical Hopf bifurcation is presented. The analysis reveals an intricate stochastic bifurcation leading to several kinds of noise-driven mixed-mode oscillations at different levels of amplitude of the noise. In the limit of strong time-scale separation, five different scaling regimes for the noise amplitude are identified. As the noise amplitude is decreased, the dynamics of the system goes from the limit cycle due to self-induced stochastic resonance to the coherence resonance limit cycle, then to bursting relaxation oscillations, followed by rare clusters of several relaxation cycles (spikes), and finally to small-amplitude oscillations (or stable fixed point) with sporadic single spikes. These scenarios are corroborated by numerical simulations.