标题： 全局耦合旋转子的splay态的稳定性 显示英文标题

标题： Stability of splay states in globally coupled rotators

摘要： 由均匀放电率（{\it 展平状态}）表征的动力学状态的稳定性在受通用速度场作用的$N$个全局脉冲耦合旋转器（神经元）网络中进行了分析。特别地，我们分析了已知在无限$N$极限下处于边缘稳定的短波长模式，并表明相应的弗洛凯指数按$1/N^2$进行缩放。此外，我们发现该谱分量的符号，从而其稳定性，由速度场的平均导数的符号决定。对于漏积分-发放神经元，得到了整个谱的解析表达式。在连续速度场的中间情况下，弗洛凯指数的缩放速度比$1/N^2$更快（即按$1/N^4$缩放），并且我们甚至在比Watanabe和Strogatz在{\it 物理学 D 74 (1994) 197-253}中考虑的正弦速度场更广泛的类中发现了严格中性方向。 显示英文摘要

摘要： The stability of dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of $N$ globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyse short-wavelength modes that were known to be marginally stable in the infinite $N$ limit and show that the corresponding Floquet exponent scale as $1/N^2$. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than $1/N^2$ (namely, as $1/N^4$) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz in {\it Physica D 74 (1994) 197-253}.