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Related papers: Bifurcations in the Kuramoto model on graphs

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We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…

Adaptation and Self-Organizing Systems · Physics 2020-05-29 David Métivier , Lucas Wetzel , Shamik Gupta

Consider $n$ identical Kuramoto oscillators on a random graph. Specifically, consider \ER random graphs in which any two oscillators are bidirectionally coupled with unit strength, independently and at random, with probability $0\leq p\leq…

Dynamical Systems · Mathematics 2022-09-28 Martin Kassabov , Steven H. Strogatz , Alex Townsend

In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…

Dynamical Systems · Mathematics 2026-01-21 Ting-Yang Hsiao , Yun-Feng Lo , Winnie Wang

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…

Adaptation and Self-Organizing Systems · Physics 2015-08-19 Jason Hindes , Christopher R. Myers

We consider the Kuramoto model on sparse random networks such as the Erd\H{o}s-R\'enyi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition…

Statistical Mechanics · Physics 2019-09-04 R. Juhász , J. Kelling , G. Ódor

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…

Optimization and Control · Mathematics 2018-09-25 Saber Jafarpour , Elizabeth Y. Huang , Francesco Bullo

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…

Adaptation and Self-Organizing Systems · Physics 2017-09-13 Lia Papadopoulos , Jason Kim , Jurgen Kurths , Danielle S. Bassett

We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which can also be random. We show that the emergent patterns are…

Chaotic Dynamics · Physics 2020-09-02 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…

Dynamical Systems · Mathematics 2021-08-11 Jared C. Bronski , Thomas E. Carty , Lee DeVille

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order…

Adaptation and Self-Organizing Systems · Physics 2017-11-29 Prosenjit Kundu , Pitambar Khanra , Chittaranjan Hens , Pinaki Pal

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…

Adaptation and Self-Organizing Systems · Physics 2025-01-13 Guilherme S. Costa , Marcel Novaes , Marcus A. M. de Aguiar

We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies.…

Dynamical Systems · Mathematics 2016-02-17 A. C. Kalloniatis , M. L. Zuparic

The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type…

Dynamical Systems · Mathematics 2026-01-16 Kuan-Wei Chen , Ting-Yang Hsiao

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

The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(\omega)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs,…

Statistical Mechanics · Physics 2020-09-04 Jinha Park , B. Kahng

Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition…

Dynamical Systems · Mathematics 2026-01-12 Margherita Bertè , Tommaso Gili

Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks…

Systems and Control · Electrical Eng. & Systems 2020-04-01 Dinuka Sahabandu , Andrew Clark , Linda Bushnell , Radha Poovendran

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…

Adaptation and Self-Organizing Systems · Physics 2023-08-02 Rico Berner , Annie Lu , Igor M. Sokolov

We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…

Physics and Society · Physics 2012-07-03 Sergi Lozano , Lubos Buzna , Albert Díaz-Guilera

We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual…

Adaptation and Self-Organizing Systems · Physics 2020-04-22 Jian Gao , Konstantinos Efstathiou