Collective mode reductions for populations of coupled noisy oscillators
arXiv:1808.07833 · doi:10.1063/1.5053576
Abstract
We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the Gaussian ansatz, and (iii) a two-cumulant truncation of the circular cumulant representation of the original system's dynamics. For the latter we suggest a closure, which makes the truncation, for small noise, a rigorous first-order correction to the Ott-Antonsen ansatz, and simultaneously is a generalization of the Gaussian ansatz. The Kuramoto model with intrinsic noise, and the population of identical noisy active rotators in excitable states with the Kuramoto-type coupling, are considered as examples to test validity of these approximations. For all considered cases, the Gaussian ansatz is found to be more accurate than the Ott-Antonsen one for high-synchrony states only. The two-cumulant approximation is always superior to both other approximations.
arXiv comment7 pages, 4 figures [compared to the journal version, typo in Eq.(22) corrected]
References in corpus (7)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Analysis of a power grid using the Kuramoto-like model
- Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
- Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
- Approximate solution to the stochastic Kuramoto model
- Interplay of coupling and common noise at the transition to synchrony in oscillator populations
- Collective dynamics in two populations of noisy oscillators with asymmetric interactions
Cited by in corpus (25)
- Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
- Theta-nested gamma oscillations in next generation neural mass models
- Hybrid-type synchronization transitions: where marginal coherence, scale-free avalanches, and bistability live together
- Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series
- Two Scenarios for the Onset and Suppression of Collective Oscillations in Heterogeneous Populations of Active Rotators
- Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
- Low-dimensional dynamics of phase oscillators driven by Cauchy noise
- Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators
- Relationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements
- Phase diagram of noisy systems of coupled oscillators with a bimodal frequency distribution
- Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise
- Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
- The effects of degree distributions in random networks of Type-I neurons
- Two-community noisy Kuramoto model with general interaction strengths: Part II
- Synchronization in a System of Kuramoto Oscillators with Distributed Gaussian Noise
- Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise
- Two-community noisy Kuramoto model with general interaction strengths: Part I
- Information geometry and synchronization phase transition in Kuramoto model
- Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory
- Small and Finite Inertia in Stochastic Systems: Moment and Cumulant Formalisms
- Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators
- Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions
- Kinetic description of one-dimensional stochastic dynamics with small inertia
- A self-consistent analytical theory for rotator networks under stochastic forcing: effects of intrinsic noise and common input
- Four approaches for description of stochastic systems with small and finite inertia