Microscopic correlations in the finite-size Kuramoto model of coupled oscillators.

  title={Microscopic correlations in the finite-size Kuramoto model of coupled oscillators.},
  author={Franziska Peter and Chen Chris Gong and Arkady Pikovsky},
  journal={Physical review. E},
  volume={100 3-1},
Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced… 
1 Citations

Figures from this paper

Chimeras on a social-type network

We consider a social-type network of coupled phase oscillators. Such a network consists of an active core of mutually interacting elements, and of a flock of passive units, which follow the driving



Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model.

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular

Dynamics of oscillators globally coupled via two mean fields

The results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems.

Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.

Finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field is reported on, which microscopically is equivalent to a hypernetwork organization of interactions and argues that a transition to synchronies occurs only for finite-size ensembles and disappears in the thermodynamic limit.

System size resonance in coupled noisy systems and in the Ising model.

When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon.

Finite-size scaling in globally coupled phase oscillators with a general coupling scheme

We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and

Entrainment transition in populations of random frequency oscillators.

Simulations of locally coupled oscillators in d dimensions reveal two types of frequency entrainment: mean-field behavior at d>4 and aggregation of compact synchronized domains in three and four dimensions.

Transition to collective oscillations in finite Kuramoto ensembles.

An alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model is presented, integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.

Dynamics of Noisy Oscillator Populations beyond the Ott-Antonsen Ansatz.

A closed system of equations for the two leading cumulants, describing the dynamics of noisy ensembles, is derived and exemplify the general theory by presenting the effect of noise on the Kuramoto system and on a chimera state in two symmetrically coupled populations.

Synchronization of Network Coupled Chaotic and Oscillatory Dynamical Systems

A recent exact solution technique developed for all-to-all connected Kuramoto oscillators is extended to certain types of networks by considering large ensembles of system realizations, demonstrating that the microscopic dynamics arise from single oscillators interacting with the mean field.

Finite-size-induced transition in ensemble of globally coupled oscillators

The collective behavior of overdamped nonlinear noise-driven oscillators coupled via mean field is investigated numerically. When a coupling constant is increased, a transition in the dynamics of the