Avalanches impede synchronization of jammed oscillators
release_whle3isa2nfndkq64mn23haqdu
by
William Gilpin
2020
Abstract
Spontaneous desynchronization of coupled oscillators occurs in diverse
systems spanning from the mammalian brain to alternating current power grids.
Here, we model desynchronization using a generalization of the classical models
of nonidentical phase-coupled oscillators, which includes short-range phase
repulsion among individual oscillators. Surprisingly, we find that our model
exhibits self-organized avalanches at intermediate values of the repulsion
strength, and that these avalanches have similar statistical properties and
scaling exponents to cascades seen in real-world oscillator
ensembles---including neuronal avalanches. We show that avalanches in our
system arise due to a critical mechanism based on competition between the mean
field and local interactions, which can be recreated using a classical cellular
automaton model of traffic jams. We exactly solve our system in the
many-oscillator limit, and find that criticality arises due to the system's
strong sensitivity to small-scale noise, here arising from local rearrangements
among oscillators. Our results provide a minimal and nearly-solvable example of
complex dynamics arising in a driven critical system.
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1906.05514v2
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