Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization

Abstract

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step phase reduction. The collective phase sensitivity and collective phase coupling functions, which quantitatively characterize the macroscopic rhythms, are illustrated using three representative models of limit-cycle oscillators. As an important result of the theory, we demonstrate noise-induced anti-phase synchronization between macroscopic rhythms by direct numerical simulations of the three models.

19 pages, 11 figures

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• Phase synchronization between collective rhythms of fully locked oscillator groups
• Noise driven current reversal and stabilisation in the tilted ratchet potential subject to tempered stable Lévy noise
• Extracting phase coupling functions between collectively oscillating networks directly from time-series data
• Steady State Statistics of Emergent Patterns in a Ring of Oscillators