Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
Ralf Tönjes, Arkady Pikovsky
Abstract
We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.
Topics & Concepts
HarmonicsCauchy distributionWhite noiseNoise (video)MathematicsForcing (mathematics)Distribution (mathematics)HarmonicPhase (matter)Harmonic oscillatorProduct (mathematics)Mathematical analysisPhysicsQuantum mechanicsGeometryComputer scienceStatisticsVoltageArtificial intelligenceImage (mathematics)Nonlinear Dynamics and Pattern FormationChaos control and synchronizationstochastic dynamics and bifurcation