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Synchronism in Large Networks of Oscillators

Large networks of many coupled oscillators have been used as models for phenomena in diverse systems. Examples include flashing fire flies, control of animals' circadian rhythm by the suprachiasmatic nucleus, neuronal dynamics, synchronization of cardiac pace-maker cells, animals that rest with half their brain in the sleep state, chemical oscillations, oscillations in bubbly fluids, synchronization of pedestrians walking on foot bridges, clapping audiences, Josephson junction circuits, arrays of coupled lasers, and many others. This talk will demonstrate and illustrate a recently developed, very general technique [1] that reduces the study of the long time temporal behavior of these models to that of low dimensional dynamical systems (e.g., to a small number of ODEs). In particular, it is shown [2] that all the possible long-time behaviors and their bifurcations are captured by this technique. Discussion of the basic mechanism responsible for this reduction and of extensions (e.g., spatio-temporal patterning models) will also be presented.

[1] E.Ott and T.M.Antonsen, Chaos (2008).
[2] E.Ott and T.M.Antonsen, Chaos (2009).

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