Ermentrout B
Department of Mathematics, University of Pittsburgh, PA 15260, USA.
Neural Comput. 1996 Jul 1;8(5):979-1001. doi: 10.1162/neco.1996.8.5.979.
Type I membrane oscillators such as the Connor model (Connor et al. 1977) and the Morris-Lecar model (Morris and Lecar 1981) admit very low frequency oscillations near the critical applied current. Hansel et al. (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions.
第一类膜振荡器，如康纳模型（康纳等人，1977年）和莫里斯 - 勒卡尔模型（莫里斯和勒卡尔，1981年），在临界施加电流附近允许非常低频的振荡。汉塞尔等人（1995年）通过数值模拟表明，使用这些模型很难实现同步，并且相位重置曲线严格为正。我们使用奇异摄动方法和平均法来表明这是第一类膜模型的一个普遍特性。我们在有限的意义上表明，通过霍普夫分岔获得节律性的模型会出现所谓的第二类重置。我们还展示了快速作用的突触和缓慢作用的突触之间的差异，并推导了相位相互作用的规范形式。
