Galán Roberto F
Department of Neurosciences, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036113. doi: 10.1103/PhysRevE.80.036113. Epub 2009 Sep 17.
We provide an analytical expression for the mean frequency shift in phase oscillators as a function of the standard deviation, sigma and the autocorrelation time, tau of small random perturbations. We show that the frequency shift is negative and proportional to sigma;{2} . Its absolute value increases monotonically with tau , approaching an asymptote determined by the L2 -norm of the phase-response curve. We validate our theoretical predictions with computer simulations and discuss their implications for the design of electronic oscillators and for the encoding of information in biological neural networks.
我们给出了相位振荡器中平均频率偏移的解析表达式，它是标准差σ和小随机扰动的自相关时间τ的函数。我们表明，频率偏移为负且与σ²成正比。其绝对值随τ单调增加，趋近于由相位响应曲线的L2范数确定的渐近线。我们通过计算机模拟验证了我们的理论预测，并讨论了它们对电子振荡器设计以及生物神经网络中信息编码的意义。
