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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

We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…

Dynamical Systems · Mathematics 2026-05-29 Ting-Yang Hsiao , Yun-Feng Lo , Chengbin Zhu

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…

chao-dyn · Physics 2009-10-31 Zhigang Zheng , Gang Hu , Bambi Hu

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and…

Chaotic Dynamics · Physics 2015-06-05 Hiroyasu Ando , Hiromichi Suetani , Juergen Kurths , Kazuyuki Aihara

The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…

Adaptation and Self-Organizing Systems · Physics 2021-09-15 M. Manoranjani , Shamik Gupta , V. K. Chandrasekar

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and…

Disordered Systems and Neural Networks · Physics 2015-05-18 Ralf Toenjes

The second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less…

Statistical Mechanics · Physics 2023-01-16 Géza Ódor , Shengfeng Deng

In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a…

Optimization and Control · Mathematics 2018-11-29 Marcello Colombino , Dominic Groß , Jean-Sébastien Brouillon , Florian Dörfler

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

When modeling the classical Kuramoto model, one of the key features is the tendency to synchronize. Accordingly, the most well-adopted choice of the coupling function is the sine function. Due to the oddness of the sine function, the…

Dynamical Systems · Mathematics 2024-04-02 Chun-Hsiung Hsia , Chung-En Tsai

We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…

Adaptation and Self-Organizing Systems · Physics 2015-05-13 Hidetsugu Sakaguchi

We study the interplay between non-Hermitian dynamics and phase synchronization in a system of $\mathcal{N}$ bosonic modes coupled to an auxiliary mode. The linearity of the evolution in such a system allows for the derivation of fully…

Quantum Physics · Physics 2021-11-04 J. Rohn , K. P. Schmidt , C. Genes

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase…

Adaptation and Self-Organizing Systems · Physics 2025-10-22 Iván León , Riccardo Muolo , Shigefumi Hata , Hiroya Nakao

Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…

Systems and Control · Electrical Eng. & Systems 2025-07-31 Ryota Kokubo , Rui Kato , Hideaki Ishii

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a non-monotonic dependence of the…

Adaptation and Self-Organizing Systems · Physics 2013-12-06 Luce Prignano , Oleguer Sagarra , Albert Díaz-Guilera

The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand,…

Statistical Finance · Quantitative Finance 2011-11-01 Y. Ikeda , H. Aoyama , Y. Fujiwara , H. Iyetomi , K. Ogimoto , W. Souma , H. Yoshikawa

A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…

Adaptation and Self-Organizing Systems · Physics 2021-07-28 Keith A. Wiley , Peter J. Mucha , Danielle S. Bassett

Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…

Chaotic Dynamics · Physics 2017-06-19 Xiyun Zhang , Arkady Pikovsky , Zonghua Liu

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…

Statistical Mechanics · Physics 2007-05-23 Yoshiki Kuramoto , Dorjsuren Battogtokh

The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…

Statistical Mechanics · Physics 2026-03-10 Anna Gallo , Renaud Lambiotte , Timoteo Carletti