Brunel N, Hakim V
Ecole Normale Sup&eacuste;rieure, LPS, 24 rue Lhomond, 75231 Paris, Cedex 5, France.
Neural Comput. 1999 Oct 1;11(7):1621-71. doi: 10.1162/089976699300016179.
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.
我们对稀疏连接的抑制性积分发放神经元网络的动力学进行了分析研究，该网络处于单个神经元以低速率不规则发放脉冲的状态。在神经元数量趋于无穷大的极限情况下，网络在静止和振荡的全局活动状态之间呈现出急剧转变，其中神经元存在弱同步。当抑制性反馈足够强时，活动变为振荡状态。发现全局振荡的周期主要由突触时间控制，但也取决于外部输入的特性。在大型但有限的网络中，分析表明，在临界抑制阈值之上和之下通常都存在具有有限相干时间的全局振荡。在这两个不同区域中，它们的特性由系统参数的函数确定。结果与数值模拟结果吻合良好。
