Related papers: Finite-size effects in a stochastic Kuramoto model
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous…
We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte…
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm…
In this work we analyze how effects of finite size may modify the thermodynamics of a system of strongly interacting fermions that we model using an effective field theory with four-point interactions at finite temperature and density and…
We investigate the scaling properties of the order parameter and the largest nonvanishing Lyapunov exponent for the fully locked state in the Kuramoto model with a finite number $N$ of oscillators. We show that, for any finite value of $N$,…
The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among them. It has been observed that if the natural frequencies of the oscillators…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
We explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations,…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
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 interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
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…