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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…

Dynamical Systems · Mathematics 2015-11-30 Priscilla E. Greenwood , Lawrence M. Ward

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…

Chaotic Dynamics · Physics 2022-03-23 Joydeep Singha , Ramakrishna Ramaswamy

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…

Adaptation and Self-Organizing Systems · Physics 2024-10-28 Leonard M. Sander

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…

Adaptation and Self-Organizing Systems · Physics 2015-06-16 Georgi S. Medvedev

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…

Adaptation and Self-Organizing Systems · Physics 2018-08-17 Timothy Ferguson

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,…

Dynamical Systems · Mathematics 2016-06-29 Bertrand Ottino-Loffler , Steven Strogatz

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…

Dynamical Systems · Mathematics 2023-08-02 Christian Bick , Tobias Böhle , Christian Kuehn

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…

Combinatorics · Mathematics 2019-09-04 Tianran Chen

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…

Dynamical Systems · Mathematics 2018-06-15 Wenlian Lu , Fatihcan M. Atay

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…

Adaptation and Self-Organizing Systems · Physics 2019-08-13 Robin Delabays , Philippe Jacquod , Florian Dörfler

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…

Chaotic Dynamics · Physics 2010-08-04 Karol Trojanowski , Lech Longa

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…

Pattern Formation and Solitons · Physics 2009-11-07 H. Yamada

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.

Physics and Society · Physics 2023-09-22 Raul J Mondragon

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…

Systems and Control · Electrical Eng. & Systems 2025-04-28 Adnan Tahirovic

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…

Adaptation and Self-Organizing Systems · Physics 2020-04-08 Shuyang Ling

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…

Adaptation and Self-Organizing Systems · Physics 2025-05-16 Seungjae Lee , Lucas Braun , Frieder Bönisch , Malte Schröder , Moritz Thümler , Marc Timme

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…

Optimization and Control · Mathematics 2007-05-23 Ali Jadbabaie , Nader Motee , Mauricio Barahona

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…

Adaptation and Self-Organizing Systems · Physics 2024-05-01 Moritz Thümler , Shesha G. M. Srinivas , Malte Schröder , Marc Timme

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…

Adaptation and Self-Organizing Systems · Physics 2010-06-30 J. Ochab , P. F. Góra

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…

Chaotic Dynamics · Physics 2024-08-30 Esmaeil Mahdavi , Mina Zarei , Farhad Shahbazi