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An incorporation of higher-order interactions is known to lead an abrupt first-order transition to synchronization in otherwise smooth second-order one for pair-wise coupled systems. Here, we show that adaptation in higher-order coupling…

Adaptation and Self-Organizing Systems · Physics 2023-02-24 Priyanka Rajwani , Ayushi Suman , Sarika Jalan

Employing the Kuramoto model as an illustrative example, we show how the use of the mean field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen [Chaos 19,…

Chaotic Dynamics · Physics 2014-11-05 Juan G. Restrepo , Edward Ott

We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…

Pattern Formation and Solitons · Physics 2015-05-21 Georg A. Gottwald

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

Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…

Machine Learning · Computer Science 2026-03-11 Yue Song , T. Anderson Keller , Sevan Brodjian , Takeru Miyato , Yisong Yue , Pietro Perona , Max Welling

The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units…

Adaptation and Self-Organizing Systems · Physics 2019-01-09 Sarthak Chandra , Michelle Girvan , Edward Ott

Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…

Populations and Evolution · Quantitative Biology 2020-05-01 Elizabeth A. Tripp , Feng Fu , Scott D. Pauls

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…

Adaptation and Self-Organizing Systems · Physics 2016-01-19 Francisco A. Rodrigues , Thomas K. DM. Peron , Peng Ji , Jürgen Kurths

The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…

Adaptation and Self-Organizing Systems · Physics 2023-04-20 Bastian Pietras , Nicolás Deschle , Andreas Daffertshofer

We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with bimodal distribution of frequencies and asymmetry between two distribution components. The…

Pattern Formation and Solitons · Physics 2023-08-03 V. A. Kostin , V. O. Munyaev , G. V. Osipov , L. A. Smirnov

We consider a variant of the Kuramoto model, in which all the oscillators are now assumed to have the same natural frequency, but some of them are negatively coupled to the mean field. These "contrarian" oscillators tend to align in…

Chaotic Dynamics · Physics 2015-05-30 Hyunsuk Hong , Steven H. Strogatz

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

Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective…

Adaptation and Self-Organizing Systems · Physics 2017-01-11 Hongbin Chen , Yuting Sun , Jian Gao , Can Xu , Zhigang Zheng

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

The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…

Dynamical Systems · Mathematics 2013-02-05 Hayato Chiba

In this numerical work we have systematically studied the dynamical phase transitions in the Kuramoto- Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the numerical steady state…

Statistical Mechanics · Physics 2018-08-07 Amitava Banerjee , Muktish Acharyya

We present a framework for controlling the collective phase of a system of coupled oscillators described by the Kuramoto model under the influence of a periodic external input by combining the methods of dynamical reduction and optimal…

Adaptation and Self-Organizing Systems · Physics 2025-04-15 Narumi Fujii , Hiroya Nakao

Swarmalators are oscillators that swarm through space as they synchronize in time. Introduced a few years ago to model many systems which mix synchrony with self-assembly, they remain poorly understood theoretically. Here we obtain the…

Adaptation and Self-Organizing Systems · Physics 2023-12-27 Kevin O'Keeffe , Gourab Kumar Sar , Md Sayeed Anwar , Joao U. F. Lizárraga , Marcus A. M. de Aguiar , Dibakar Ghosh

We explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at…

Statistical Mechanics · Physics 2025-07-21 Anish Acharya , Mrinal Sarkar , Shamik Gupta

We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a…

Chaotic Dynamics · Physics 2016-06-22 Kevin P. O'Keeffe , Steven H. Strogatz