Bressloff P C, Bressloff N W, Cowan J D
Department of Mathematical Sciences, Loughborough University, Leicestershire, UK.
Neural Comput. 2000 Nov;12(11):2473-511. doi: 10.1162/089976600300014809.
Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous state to a non-phase-locked state whose spike trains are characterized by clustered but irregular fluctuations of the interspike intervals (ISIs). The separation of these clusters in phase space results in a localized peak of activity as measured by the time-averaged firing rate of the neurons. This generates a sharp orientation tuning curve that can lock to a slowly rotating, weakly tuned external stimulus. Under certain conditions, the peak can slowly rotate even to a fixed external stimulus. The ring also exhibits hysteresis due to the subcritical nature of the bifurcation to sharp orientation tuning. Such behavior is shown to be consistent with a corresponding analog version of the IF model in the limit of slow synaptic interactions. For fast synapses, the deterministic fluctuations of the ISIs associated with the tuning curve can support a coefficient of variation of order unity.
从自发模式形成的角度分析了脉冲耦合积分发放（IF）神经元环中的方向调谐。展示了该环如何从同步状态分叉到非锁相状态，其脉冲序列的特征是峰峰间隔（ISI）存在聚类但不规则的波动。这些聚类在相空间中的分离导致了神经元时间平均发放率所测量的局部活动峰值。这产生了一条尖锐的方向调谐曲线，该曲线可以锁定到缓慢旋转、弱调谐的外部刺激。在某些条件下，即使对于固定的外部刺激，峰值也可以缓慢旋转。由于分叉到尖锐方向调谐的亚临界性质，该环还表现出滞后现象。这种行为被证明与慢突触相互作用极限下IF模型的相应模拟版本一致。对于快速突触，与调谐曲线相关的ISI的确定性波动可以支持量级为1的变异系数。
