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Related papers: On the Critical Coupling for Kuramoto Oscillators

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We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…

Adaptation and Self-Organizing Systems · Physics 2018-04-04 Franziska Peter , Arkady Pikovsky

The Kuramoto model serves as a paradigm to study the phenomenon of spontaneous collective synchronization. We study here a nontrivial generalization of the Kuramoto model by including an interaction that breaks explicitly the rotational…

Adaptation and Self-Organizing Systems · Physics 2020-09-30 V K Chandrasekar , M Manoranjani , Shamik Gupta

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…

Pattern Formation and Solitons · Physics 2009-11-13 Renato Mirollo , Steven H. Strogatz

We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…

Adaptation and Self-Organizing Systems · Physics 2024-07-19 Arkady Pikovsky , Franco Bagnoli

We investigate the synchronized collective behavior of the Kuramoto oscillators with inertia effect. Both the frequency synchronization for nonidentical case and the phase synchronization for identical case are in view. As an application of…

Dynamical Systems · Mathematics 2018-01-01 Chun-Hsiung Hsia , Chang-Yeol Jung , Bongsuk Kwon

The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…

Disordered Systems and Neural Networks · Physics 2009-08-25 R. Toenjes , B. Blasius

We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a…

Statistical Mechanics · Physics 2014-07-11 Shamik Gupta , Alessandro Campa , Stefano Ruffo

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

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,…

Statistical Mechanics · Physics 2025-05-12 Zhongpu Qiu , Tianyi Wu , Sheng Fang , Jun Meng , Jingfang Fan

We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak…

Adaptation and Self-Organizing Systems · Physics 2023-03-29 Wei Zou , Sujuan He , D. V. Senthilkumar , Juergen Kurths

We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for…

Adaptation and Self-Organizing Systems · Physics 2016-08-31 Amitava Banerjee , Muktish Acharyya

The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…

Mathematical Physics · Physics 2024-03-26 Yagmur Kati , Jonas Ranft , Benjamin Lindner

We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…

Disordered Systems and Neural Networks · Physics 2017-05-23 Sara Ameli , Farhad Shahbazi , Maryam Karimian , Tahereh Malakoutikhah

Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…

Physics and Society · Physics 2024-06-14 Guilherme S. Costa , Marcus A. M. de Aguiar

The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…

Probability · Mathematics 2024-02-16 Pedro Abdalla , Afonso S. Bandeira , Clara Invernizzi

In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…

Pattern Formation and Solitons · Physics 2009-11-13 Markus Brede

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

The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important…

Adaptation and Self-Organizing Systems · Physics 2021-06-30 Jared Bronski , Lan Wang

Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition…

Adaptation and Self-Organizing Systems · Physics 2024-06-19 Marios Antonios Gkogkas , Benjamin Jüttner , Christian Kuehn , Erik Andreas Martens

Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency…

Pattern Formation and Solitons · Physics 2013-05-30 M. C. Cross