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Updated: Jun 30, 2026

Generation of Local CA1 γ Oscillations by Tetanic Stimulation
Published on: August 14, 2015
Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron
Martin Krupa1, Nikola Popović, Nancy Kopell
1Department of Mathematical Sciences, New Mexico State University, P.O. Box 30001, Department 3MB, Las Cruces, New Mexico 88003, USA. mkrupa@nmsu.edu
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form that can be analyzed via a slight adaptation of the approach developed by M. Krupa, N. Popovic, and N. Kopell (unpublished).
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