We analytically investigate the stability of splay states in the networks of N globally pulse-coupled phase-like models of neurons. We develop a perturbative technique which allows determining the Floquet exponents for a generic velocity field and implement the method for a given pulse shape. We find that in the case of discontinuous velocity fields, the Floquet spectrum scales as 1 / N 2 and the stability is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape, but it is independent of the velocity field.PACS:05.45.Xt, 84.35.+i, 87.19.lj.
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机译：我们分析性地研究了神经元的N个全局脉冲耦合相位样模型网络中张弛状态的稳定性。我们开发了一种微扰技术，可以确定通用速度场的Floquet指数，并针对给定的脉冲形状实现该方法。我们发现，在不连续速度场的情况下，Floquet谱缩放为1 / N 2，并且稳定性由不连续处的跳跃符号决定。总而言之，频谱的形式取决于脉冲形状，但与速度场无关.PACS：05.45.Xt，84.35。+ i，87.19.lj.
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