Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators.

  title={Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators.},
  author={Iv'an Le'on and Diego Paz'o},
  volume={32 6},
The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be applied, and the heterogeneity is distributed following a rational function. In this work, we demonstrate the usefulness of a moment-based scheme to reproduce the dynamics of infinitely many oscillators. Our analysis is particularized for Gaussian heterogeneities, leading to a Fourier-Hermite… 

Figures from this paper


Enlarged Kuramoto model: Secondary instability and transition to collective chaos.
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase
Dynamics in the Sakaguchi-Kuramoto model with bimodal frequency distribution
This work reduces the globally coupled phase oscillators to low dimensional coupled ordinary differential equations by using Ott-Antonsen ansatz and analyzes the stabilities of the incoherent state and different partial synchronous states in the Sakaguchi-Kuramoto model.
Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation.
An isochron-based scheme is developed to obtain the second-order phase approximation, which reproduces the weak-coupling dynamics of the MF-CGLE at moderate coupling.
Oscillator glass in the generalized Kuramoto model: synchronous disorder and two-step relaxation
We consider a very general form of the Kuramoto model (KM) and derive equations for the macroscopic parameters of its stationary states. Surprisingly, we discover that a class of simple, analytically
Cooperative Phenomena in Coupled Oscillator Systems under External Fields
Systems of many limit cycle oscillators are studied by using a phase description of the oscillation. Each oscillator interacts with all the other oscillators uniformly and is subject to external
Phase transitions in active rotator systems
On introduit un modele de rotateur actif afin d'etudier la dynamique statistique d'une grande population d'oscillateurs a cycle limite ou d'elements excitables. Ceci se definit dynamiquement comme
Critical Conditions of Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators
On the basis of the order function theory developed previously, critical conditions are derived and numerically verified for the onset of macroscopic mutual entrainment in phase models of uniformly
Chemical Oscillations, Waves, and Turbulence
Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes.
This analysis of the collective dynamics of a large ensembles of dynamical units with nonpairwise interactions, namely coupled phase oscillators with three-way interactions, sheds light on the complexity that can arise in physical systems with simplicial interactions like the human brain and the role that simplified interactions play in storing information.