A Period-adding Bifurcation in a Pair of Coupled Neurons

When: Wednesday, February 29, 2012, 11:30am-12:20 pm
Where: Olin Hall 321
Presenter: Thomas LoFaro

In this talk on work done with my thesis advisor Nancy Kopell, I will discuss a neurophysiological model of a pair of coupled neurons that exhibits a period-adding phenomenon in response to the variation of a parameter in the model equations. The motivating example comes from a subnetwork of two neurons in the crustacean stomatogastric ganglia (STG) that are coupled via reciprocal inhibition. We show that when one of these neurons possesses a hyperpolarization-activated inward current (i_h) then these neurons may exhibit a type of subharmonic coordination where only n:1 firing rhythms occur. This is in contrast to a typical pair of coupled oscillators where n:m subharmonics may occur for all pairs of integers n and m.

Geometric singular perturbation techniques are used to reduce a high-dimensional system of differential equations to a much smaller dimensional map whose dynamics are more easily understood. This reduction gives insight into the critical role of i_h in coordinating and regulating the network rhythms.

Thomas LoFaro is Professor of Mathematics and Computer Science at Gustavus Adolphus College.

Lunch will be served.

This presentation is part of the MCS Seminar series; please see the calendar of upcoming events. Also, please email suggestions for future seminars as well as any questions.