Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
arXiv:2009.04725 · doi:10.1103/PhysRevE.102.052315
Abstract
We study an 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.
5 pages, 2 figures
References in corpus (3)
Cited by in corpus (13)
- Exact finite-dimensional description for networks of globally coupled spiking neurons
- Coherence resonance in influencer networks
- Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
- Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between
- Effect of Cauchy noise on a network of quadratic integrate-and-fire neurons with non-Cauchy heterogeneities
- Exact low-dimensional description for fast neural oscillations with low firing rates
- Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories
- Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise
- Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise
- Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
- Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise
- Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons
- Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons