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arXiv · 1411.3204

Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

Vladimir Vlasov·Maxim Komarov·Arkady Pikovsky
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Abstract

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and synchronous solutions, and also appearance of symmetric two-cluster solution which can coexist with regular synchronous state. Remarkably, we show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastable asynchronous solution.

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Vladimir Vlasov, Maxim Komarov, Arkady Pikovsky. 2014-11-12. Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling. https://doi.org/10.1088/1751-8113%2F48%2F10%2F105101

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