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Type I Membranes, Phase Resetting Curves, and Synchrony (1995)
| Venue: | Neural Comput |
| Citations: | 203 - 12 self |
BibTeX
@ARTICLE{Ermentrout95typei,
author = {Bard Ermentrout},
title = {Type I Membranes, Phase Resetting Curves, and Synchrony},
journal = {Neural Comput},
year = {1995},
volume = {8},
pages = {979--1001}
}
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Abstract
Type I membrane oscillators such as the Connor model (Connor, Walter, and McKown, 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 2 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. 1 Introduction The behavior of coupled neural oscillators has been the subject of a great deal of recent interest. In general, this behavior is quite difficult to analyze. Most of the results to date are primarily based on simulations of ...
