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Self-sustaining oscillations in complex networks of excitable elements
Patrick McGraw1, Michael Menzinger
1Department of Chemistry, University of Toronto, Toronto, Ontario M5S3H6, Canada.
Abstract:
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as driving loops in which the excitation periodically circulates. We analyze the mechanism, describe the oscillating states, identify the pacemaker loops, and explain key features of their distribution.
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