Lindner Benjamin, Doiron Brent, Longtin André
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Canada K1N-6N5.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 1):061919. doi: 10.1103/PhysRevE.72.061919. Epub 2005 Dec 29.
A network of leaky integrate-and-fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied. We calculate the spectral statistics of the network (power spectrum of the population activity, cross spectrum between spike trains of different neurons) as well as of a single neuron (power spectrum of spike train, cross spectrum between external noise and spike train) within the network. As shown by comparison with numerical simulations, our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise. By means of our analytical results we discuss the quality of the correlation-induced oscillation in a large network as a function of the transmission delay and the internal noise intensity. It is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay (i.e., the delay period is longer than any other time scale in the system). For a neuron with a strong intrinsic frequency, the oscillation becomes strongly anharmonic in the case of a long delay time. We also discuss briefly the kind of synchrony introduced by the feedback-induced oscillation.
研究了一个具有全局抑制性反馈且受空间相关噪声影响的漏电积分发放神经元网络。我们计算了网络的频谱统计量（群体活动的功率谱、不同神经元脉冲序列之间的互谱）以及网络内单个神经元的频谱统计量（脉冲序列的功率谱、外部噪声与脉冲序列之间的互谱）。与数值模拟结果对比表明，如果反馈较弱且外部噪声量不超过内部噪声量，我们的理论对于任意网络规模都能很好地适用。借助我们的分析结果，我们讨论了大网络中相关性诱导振荡的质量与传输延迟和内部噪声强度的函数关系。结果表明，在内部噪声为零且绝热延迟时间很长（即延迟周期长于系统中的任何其他时间尺度）的系统中可获得最强的振荡。对于具有强固有频率的神经元，在延迟时间较长的情况下，振荡会变得强烈非谐。我们还简要讨论了反馈诱导振荡所引入的同步类型。
