PARABOLIC BURSTING IN AN EXCITABLE SYSTEM COUPLED WITH A SLOW OSCILLATION
PARABOLIC BURSTING IN AN EXCITABLE SYSTEM COUPLED WITH A SLOW OSCILLATION
复制标题
DOI：
10.1137/0146017
复制
发表时间：
1986-04-01
影响因子：
1.9
通讯作者：
KOPELL, N
中科院分区：
文献类型：
--
作者：
ERMENTROUT, GB;KOPELL, N
研究了一个可激发系统与慢振荡系统的相互作用。在与通常关于可兴奋系统的更严格的假设相容的鲁棒和一般假设下，我们证明了这样的耦合系统可以显示爆发，即一个稳定的解，其中一些变量经历快速振荡，然后是一段时间的静止，振荡和静止不断重复。在更弱的条件下，爆发是“抛物线”的，即快速振荡的本地频率增加，然后在爆发内减小。本文中的技术涉及到坐标的非线性变化，将方程转换成与Hill方程密切相关的方程。
We investigate the interaction of an excitable system with a slow oscillation. Under robust and general assumptions compatible with the more stringent assumptions usually made about excitable systems, we show that such a coupled system can display bursting, i.e. a stable solution in which some variable undergoes rapid oscillations followed by a period of quiescence, with both oscillation and quiescence continually repeated. Under a further weak condition, the bursting is “parabolic”, i.e. the local frequency of the fast oscillation increases and then decreases within a burst. The technique in this paper involves nonlinear changes of coordinates which transform the equations into ones which are closely related to Hill’s equation.