Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Document Type

Article

Publication Date

1-1-2008

Abstract

Mixed-mode dynamics is a complex type of dynamical behavior that has been observed both numerically and experimentally in numerous prototypical systems in the natural sciences. The compartmental Wilson-Callaway model for the dopaminergic neuron is an example of a system that exhibits a wide variety of mixed-mode patterns upon variation of a control parameter. One characteristic feature of this system is the presence of multiple time scales. In this article, we study the Wilson-Callaway model from a geometric point of view. We show that the observed mixed-mode dynamics is caused by a slowly varying canard structure. By appropriately transforming the model equations, we reduce them to an underlying three-dimensional canonical form that can be analyzed via a slight adaptation of the approach developed by M. Krupa, N. Popović, and N. Kopell (unpublished). © 2008 American Institute of Physics.

Identifier

41549122782 (Scopus)

Publication Title

Chaos

External Full Text Location

https://doi.org/10.1063/1.2779859

ISSN

10541500

Issue

1

Volume

18

Grant

DMS-0211505

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS