脉冲耦合网络中张开态的稳定性
Stability of the splay state in pulse--coupled networks
摘要：
在一个全局耦合的漏积分-激发神经元网络中，分析了具有均匀激发率的动力学状态（{ \it splay states}）的稳定性.这是通过将微分方程组简化为在大网络尺寸的限制下研究的映射来完成的。我们表明，splay状态的稳定性取决于至关重要的脉冲宽度和尖峰间隔之间的比率。更准确地说，Floquet指数的频谱原来是由三个组成部分：（i）一个与平均场分析[Abbott-van Vreesvijk，1993年]的预测相一致，（ii）一个分量测量的“有限频率”模式的不稳定性;（iii）与单个脉冲的特性相关的一些“孤立”本征值，这些本征值可能引起强不稳定性。（Floquet指数与网络大小成比例）。最后，作为一个副结果，我们发现，即使抑制耦合的splay状态可以是稳定的。
英文摘要：
The stability of the dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse--width and the inter-spike interval. More precisely, the spectrum of Floquet exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott-van Vreesvijk, 1993]; (ii) a component measuring the instability of "finite-frequency" modes; (iii) a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.
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