标题： 脉冲耦合神经元网络中splay状态的稳定性 显示英文标题

标题： Stability of the splay state in networks of pulse-coupled neurons

摘要： 我们通过解析方法研究了网络中{\it 展开状态}的稳定性，这些网络由$N$脉冲耦合的类似相位的神经元模型组成。 通过开发一种微扰技术，我们发现，在$N$很大的极限情况下，Floquet 谱按$1/N^2$缩放，对于一般的不连续速度场而言。 此外，所谓的短波长分量的稳定性由不连续处跳跃的符号决定。 总的来说，谱的形式取决于脉冲形状，但与速度场无关。 显示英文摘要

摘要： We analytically investigate the stability of {\it splay states} in networks of $N$ pulse-coupled phase-like models of neurons. By developing a perturbative technique, we find that, in the limit of large $N$, the Floquet spectrum scales as $1/N^2$ for generic discontinuous velocity fields. Moreover, the stability of the so-called short-wavelength component is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape but is independent of the velocity field.