Return map characterizations for a model of bursting with two slow variables

Authors

Mark Pernarowski, Montana State University

Document Type

Presentation Abstract

Presentation Date

10-16-2003

Abstract

Many neurons and endocrine cells exhibit periodic bursting oscillations in their transmembrane electrical potential. The fast subsystems of the corresponding models exhibit bistability between stable equilibria and periodic orbits. Slow variables evolve in a manner which causes the solutions to switch between pseudo-stationary and oscillatory states resulting in a characteristic bursting pattern.

Most recent models involve two slow variables which tends to complicate their analyses. Using singular perturbation techniques we show that bursting solutions of such models correspond to fixed points of a one dimensional map constructed from the fast and slow subsystems. We further show that for some parameter values, bistability between bursting solutions and stable equilibria is possible.

Additional Details

Thursday, 16 October 2003
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. in Math 104

Recommended Citation

Pernarowski, Mark, "Return map characterizations for a model of bursting with two slow variables" (2003). Colloquia of the Department of Mathematical Sciences. 148.
https://scholarworks.umt.edu/mathcolloquia/148