Related papers: Finite-size scaling of synchronized oscillation on…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…
In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
We numerically study the synchronization of an identical population of Kuramoto-Sakaguchi phase oscillators in Watts-Strogatz networks. We find that, unlike random networks, phase-shift could enhance the synchronization in small-world…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic…
Based on a local greedy numerical algorithm, we compute the topology of weighted, directed, and of unlimited extension networks of non identical Kuramoto oscillators which simultaneously satisfy 2 criteria: i) global frequency…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
We study rare phase slips due to noise in synchronized Kuramoto oscillator networks. In the small-noise limit, we demonstrate that slips occur via large fluctuations to saddle phase-locked states. For tree topologies, slips appear between…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of…
Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…