Graduate student seminar | Bifurcations of Large Networks of Pulse-Coupled Oscillators

Speaker

Wilten Nicola, PhD Candidate
Department of Applied Mathematics, University of Waterloo

Abstract

Many functional subunits of the brain contain a large number of neurons. These regions are often modeled as networks of pulsecoupled oscillators. The models can be conductance based or of the integrate-and-fire type. When fit properly, these large network models replicate the bifurcations of the original data. Since these models are non-smooth systems, determining the bifurcation types of these networks is outside the realm of classical bifurcation theory. Population density equations extend the classical theory to these systems. The theory is applied to a model consisting of a network of Izhikevich neurons fit to hippocampal region CA3.

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