全局耦合旋转体中splay态的稳定性
Stability of splay states in globally coupled rotators
摘要：
在一般速度场作用下，分析了由$N$全局脉冲耦合旋转子（神经元）组成的网络中，以均匀放电率（{ \it splay states}）为特征的动力学状态的稳定性.特别是，我们分析短波长模式，已知是边际稳定的无限$N$限制，并显示相应的Floquet指数规模为$1/N^2$。此外，我们发现，该谱分量的符号，从而稳定性，是由速度场的平均导数的符号。对于漏积分激发神经元，得到了整个谱的解析表达式。在连续速度场的中间情况下，Floquet指数的标度比$1/N^2$（即，作为$1/N^4$）更快，并且我们甚至在比Watanabe和Strogatz在{ \it Physica D 74（1994）197-253}中考虑的正弦速度场更广泛的类别中发现严格中性方向。
英文摘要：
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}.
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