COLLECTIVE SYNCHRONIZATION OF PULSE-COUPLED OSCILLATORS AND EXCITABLE UNITS
COLLECTIVE SYNCHRONIZATION OF PULSE-COUPLED OSCILLATORS AND EXCITABLE UNITS
复制标题
DOI：
10.1016/0167-2789(91)90075-k
复制
发表时间：
1991-05-01
期刊：
影响因子：
4
通讯作者：
KURAMOTO, Y
中科院分区：
文献类型：
--
作者：
KURAMOTO, Y
本文提出并研究了一类具有脉冲耦合的积分激发型振子和可激发单元的相位模型。 这些单元会受到外部噪声的影响，并且它们的相互连接是全面的。 导出了封闭形式的相分布演化方程。 在弱噪声极限下的稳态分析表明了集体双稳态的可能性。 当耦合和噪声足够弱时，演化方程大大简化。 这种方程的简化使得能够进行各种量的分析计算。 其中，稳定的分布的稳定性进行了明确的分析，和集体振荡的发病描述的霍普夫分岔。 通过引入绝对耐火度，本文模型在某些方面得到了改进。
A phase model is proposed and studied for a population of integrate-and-fire-type oscillators and excitable units with pulsatile coupling. The units are subject to external noise, and their mutual connection is all-to-all. An evolution equation is derived for the phase distribution in a closed form. Its steady-state analysis in the limit of weak noise shows the possibility of collective bistability. The evolution equation is simplified drastically when the coupling as well as noise is sufficiently weak. This reduction of equation enables analytical calculation of various quantities. Among others, the stability of the steady distribution is analyzed explicitly, and the onset of collective oscillations is described in terms of the Hopf bifurcation. It is also shown that the present model is improved in some respects by introducing absolute refractoriness.