Synchronization of Phase Oscillators on the Hierarchical Lattice

@article{Garlaschelli2018SynchronizationOP,
  title={Synchronization of Phase Oscillators on the Hierarchical Lattice},
  author={Diego Garlaschelli and Frank den Hollander and Janusz M. Meylahn and Benthen Zeegers},
  journal={Journal of Statistical Physics},
  year={2018},
  volume={174},
  pages={188-218}
}
Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network, namely, the hierarchical lattice. Each site of the lattice carries an oscillator that is subject to noise. Pairs of oscillators interact with each other at a strength that depends on their hierarchical distance, modulated by a sequence of interaction… 

Two-community noisy Kuramoto model

We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative (but not zero). We find that, in

Collective Behavior in Dynamics on Networks

  • Physics
  • 2019
Collective Behavior in Dynamics on Networks This dissertation addresses three problems concerning collective behavior in dynamics on networks: coupling in a heterogeneous population of oscillators

UvA-DARE (Digital Academic Repository) Two-community noisy Kuramoto model with general interaction strengths. II Two-community noisy Kuramoto model with general interaction strengths: Part II

We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

Synchronization of the asymmetrical system with three non-identical Kuramoto oscillators: models of solar meridional circulation

Модели Курамото нелинейно связанных осцилляторов позволяют достаточно просто описывать фазовую синхронизацию в сложных системах. В данной работе мы рассматриваем частный случай модели Курамото с

References

SHOWING 1-10 OF 23 REFERENCES

The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is

Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model

The aim of the paper is to address the long time behavior of the Kuramoto model of mean-field coupled phase rotators, subject to white noise and quenched frequencies. We analyse the influence of the

Long time behavior of a spherical mean field model

In this thesis, we study some aspects of the long time behavior of a spherical mean field model. This model is motivated by problems in mathematical physics and statistical mechanics. More precisely,

Synchronization and random long time dynamics for mean-field plane rotators

We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition

Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping.

This work analyzes a model of globally coupled nonlinear oscillators with randomly distributed frequencies and proves that, for coupling strengths below a certain threshold, this system would always relax to an incoherent state.

Approximate solution to the stochastic Kuramoto model.

The Kuramoto phase oscillators can be reduced in a Gaussian approximation to two first-order differential equations to yield a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators.

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