Phase Models for Oscillators with Time Delayed Coupling

Sue Ann Campbell (March 24, 2011)

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Abstract

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. Numerical bifurcation analysis of the full system of delay differential equations is used determine constraints on the coupling strength such that the phase model is valid. Both type I and type II oscillators are considered.