Spectral Analysis of Stochastic Phase Lockings and Stochastic Bifurcations in the Sinusoidally Forced van der Pol Oscillator with Additive Noise
Spectral Analysis of Stochastic Phase Lockings and Stochastic Bifurcations in the Sinusoidally Forced van der Pol Oscillator with Additive Noise
复制标题
具有加性噪声的正弦强制范德波尔振荡器中随机锁相和随机分岔的频谱分析
DOI：
10.1023/a:1023271109747
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发表时间：
1998
影响因子：
1.6
通讯作者：
S. Kumagai
中科院分区：
文献类型：
--
作者：
S. Doi;Junko Inoue;S. Kumagai
研究了噪声对正弦受迫范德波尔弛豫振子的相位锁定和分叉的影响。将确定性(无噪声)一维Poincaré映射推广到由随机核函数定义的算子的迭代。根据算符的密度演化，分析了随机相定位和随机分叉。特别地，提出了一种利用算子的谱(特征值和特征函数)来集中分析随机分支的新方法。
Noise effects on the phase lockings and bifurcations in the sinusoidally forced van der Pol relaxation oscillator are investigated. Deterministic (noise-free) one-dimensional Poincaré mapping is extended to the iteration of the operator defined by a stochastic kernel function. Stochastic phase lockings and bifurcations are analyzed in terms of the density evolution by the operator. In particular, a new method which uses spectra (eigenvalues and eigenfunctions) of the operator to analyze stochastic bifurcations intensively is proposed.