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Dynamics of large oscillator populations with random interactions
Arkady Pikovsky1, Lev A Smirnov2
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
Abstract:
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions defined via the coupling functions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function.
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