Related papers: Phase-locked Patterns of the Kuramoto Model on 3-R…
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…
We examine the dynamics of an ensemble of phase oscillators that are divided in $k$ sets, with time-delayed coupling interactions {\em only} between oscillators in different sets or partitions. The network of interactions thus form a…
We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not…
The Kuramoto model of coupled phase oscillators on small-world (SW) graphs is analyzed in this work. When the number of oscillators in the network goes to infinity, the model acquires a family of steady state solutions of degree q, called…
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 study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, $N$, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case,…
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
In this note we show that for the Kuramoto model defined in a simple undirected graph it is possible to decide which nodes form the core of the network. The set of core-nodes is defined by its relevance to the phase synchronisation process.
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
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…
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…
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…
We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and…