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Society for Mathematical Biology Conference
July 30 - August 2, 2008
Centre for Mathematical Medicine, Fields Institute
Toronto, Canada

Organizers
Organizing Committee: S.Sivaloganathan-Chair(Waterloo), M.Kohandel (Waterloo), I.Pressman(Carleton), F.Skinner(Toronto Western Research Inst.), H. Zhu(York)

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Phase Models with Time Delay
by
Sue Ann Campbell
University of Waterloo
Coauthors: Ilya Kobelevskiy and Andrew Smith

We consider a network of inherently oscillatory neurons with time delayed connections. We reduce the system of delay differential equations to a phase model representation and show how the time delay enters into the reduced model. For the case of two neurons, we show how the time delay may affect the stability of the periodic solution leading to stability switching between synchronous and antiphase solutions as the delay is increased. The results of the phase model analysis are compared with numerical bifurcation analysis of the full system of delay differential equations. Both type I and type II oscillators are considered.

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Date received: May 6, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-55.