Colloquium

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

Mark Pernarowski Montana State University

M any 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. M ost 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.

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

Fall 2003 Colloquium Schedule          Mathematical Sciences | The University of Montana