Front Propagation in Stochastic Neural Fields
Front Propagation in Stochastic Neural Fields
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DOI：
10.1137/110851031
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发表时间：
2012-01-01
影响因子：
2.1
通讯作者：
Webber, Matthew A.
中科院分区：
文献类型：
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作者：
Bressloff, Paul C.;Webber, Matthew A.
我们分析了外在乘性噪声对具有兴奋连接的标量神经场中前沿传播的影响。利用时间尺度的分离，我们用长时间尺度上锋面相对于其均匀平移位置的类扩散位移(漂移)和短时间尺度上锋面轮廓围绕其瞬时位置的起伏来表示起伏锋面。我们分析的一个主要结果是比较了自由传播的前锋和锁定在外部运动刺激下的前锋。我们证明了后者对噪声的鲁棒性要强得多，因为平均锋面轮廓的随机漂移用Ornstein-Uhlenbeck过程而不是Wiener过程来描述，因此锋面位置的方差在长时间内是饱和的，而不是随时间线性增加。最后，我们考虑了一个随机神经场，它支持确定性极限中的拉前锋，并且证明了这样的前锋的漂移现在是次扩散的。
We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive.