Wilson H R, Cowan J D
Biophys J. 1972 Jan;12(1):1-24. doi: 10.1016/S0006-3495(72)86068-5.
Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
针对包含兴奋性和抑制性模型神经元的空间局部群体动力学，推导了耦合非线性微分方程。然后使用相平面方法和数值解来研究群体对各种类型刺激的反应。所得结果显示出简单和多重滞后现象以及极限环活动。后者特别有趣，因为发现极限环振荡的频率是刺激强度的单调函数。最后，证明了对一类刺激的极限环动力学的存在意味着对另一类刺激存在多个稳定状态和滞后现象。讨论了这些发现与一些实验之间的关系。
