English
Related papers

Related papers: Small-world networks of Kuramoto oscillators

200 papers

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…

Pattern Formation and Solitons · Physics 2009-11-13 Lauren M. Childs , Steven H. Strogatz

Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite…

Optimization and Control · Mathematics 2018-09-20 Elizabeth Y. Huang , Saber Jafarpour , Francesco Bullo

The dynamics of dissipative topological defects in a system of coupled phase oscillators, arranged in one and two-dimensional arrays, is numerically investigated using the Kuramoto model. After an initial rapid decay of the number of…

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…

We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is…

Adaptation and Self-Organizing Systems · Physics 2015-06-25 Bernard Sonnenschein , Thomas K. DM. Peron , Francisco A. Rodrigues , Jürgen Kurths , Lutz Schimansky-Geier

Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…

Dynamical Systems · Mathematics 2022-09-16 Tung T. Nguyen , Roberto C. Budzinski , Jacqueline Doan , Federico W. Pasini , Jan Minac , Lyle E. Muller

Synchronization in networks of coupled oscillators is classically studied via the Kuramoto model, whose intrinsic nonlinearity limits analytical tractability and complicates control design. Complex-valued extensions circumvent this by…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Lorenzo Giordano , Josep M. Olm , Mario di Bernardo

The homogeneous Kuramoto model on a graph $G = (V,E)$ is a network of $|V|$ identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit strength) to its neighbors in the graph. A graph $G$ is said…

Combinatorics · Mathematics 2025-01-22 Vishesh Jain , Clayton Mizgerd , Mehtaab Sawhney

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…

Adaptation and Self-Organizing Systems · Physics 2024-10-24 Kevin P. O'Keeffe

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…

Adaptation and Self-Organizing Systems · Physics 2024-08-23 Md Sayeed Anwar , S. Nirmala Jenifer , Paulsamy Muruganandam , Dibakar Ghosh , Timoteo Carletti

This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…

Adaptation and Self-Organizing Systems · Physics 2025-02-04 Sara Ameli , Esmaeil Mahdavi , Mina Zarei , Farhad Shahbazi

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…

Adaptation and Self-Organizing Systems · Physics 2017-09-20 Shamik Gupta

The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…

Adaptation and Self-Organizing Systems · Physics 2022-10-05 Guilhermo L. Buzanello , Ana Elisa D. Barioni , Marcus A. M. de Aguiar

The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…

Adaptation and Self-Organizing Systems · Physics 2020-01-22 Chen Chris Gong , Arkady Pikovsky

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…

Chaotic Dynamics · Physics 2009-11-07 Edward Ott , Paul So , Ernest Barreto , Thomas Antonsen

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian…

Quantitative Methods · Quantitative Biology 2009-11-11 Jacques Rougemont , Felix Naef

The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…

Chaotic Dynamics · Physics 2013-12-04 Anandamohan Ghosh , Shamik Gupta

The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…

Adaptation and Self-Organizing Systems · Physics 2020-01-23 Inmaculada Leyva , Cristina Masoller

In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…

Statistical Mechanics · Physics 2023-10-31 Leidy Katherin Eraso Hernández , Alejandro P. Riascos

Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…

Systems and Control · Electrical Eng. & Systems 2024-03-21 Andreas Bathelt , Vimukthi Herath , Thomas Dallmann