Collective Dynamics of Deterministic and Noisy Oscillator Populations: Beyond Ott-Antonsen Theory

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Synchronization in ensembles of oscillators manifests itself as appearance of a macroscopic collective mode. In a particular situation, such a mode can be described analytically by virtue of the Ott-Antonsen approach. Our first aim in this project is to generalise this approach by constructing an effective perturbation theory near the Ott-Antonsen manifold, thus extending it to non-ideal situations. We will explore with this theory the effects which are not covered by the Ott-Antonsen equations: effects of intrinsic noise, of deterministic high-harmonics perturbations, of disorder in parameters. Our second goal is to study effects of common noise on the synchronization properties of coupled oscillators. The main attention will be devoted to situations where coupling is desynchronizing and thus competes with synchronizing action of noise. While analytical theory will be developed for simplest setups, the effects will be also tested on practically relevant systems like Josephson junctions and spin-torque oscillators.