Averaging, Folded Singularities, and Torus Canards: Explaining Transitions between Bursting and Spiking in a Coupled Neuron Model

被引：31

作者：

Roberts, Kerry-Lyn ^{[1
]}

Rubin, Jonathan E. ^{[2
,3
]}

Wechselberger, Martin ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[3] Univ Pittsburgh, Ctr Neural Basis Cognit, Pittsburgh, PA 15260 USA

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2015年 / 14卷 / 04期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

geometric singular perturbation theory; multiple time scales; averaging; folded singularities; torus canards; bursting; neuronal dynamics; RESPIRATORY RHYTHM GENERATION; PRE-BOTZINGER COMPLEX; TONIC SPIKING; OSCILLATIONS; COEXISTENCE; BIFURCATION;

D O I：

10.1137/140981770

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we identify generic bifurcation scenarios corresponding to transitions between bursting and tonic spiking solutions in a model for a coupled pair of burst-capable neurons, and we elucidate the central role of folded singularities in these scenarios. The folded singularities in our work arise in the context of fast-slow averaging, and hence our results link with the study of torus canards, a recently identified class of ordinary differential equation (ODE) solutions featuring oscillatory excursions along repelling structures in phase space [J. Burke et al., J. Math. Neurosci., 2 (2012), pp. 1-30]; in particular, our work extends this study to systems featuring two slow variables and symmetry and goes significantly beyond the analysis of activity transitions presented by Best et al. [SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 1107-1139].

引用

页码：1808 / 1844

页数：37