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We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…

Adaptation and Self-Organizing Systems · Physics 2024-11-12 Rok Cestnik , Erik A. Martens

We consider the celebrated Cucker-Smale model in finite dimension, modelling interacting collective dynamics and their possible evolution to consensus. The objective of this paper is to study the effect of time delays in the general model.…

Optimization and Control · Mathematics 2017-07-27 Cristina Pignotti , Emmanuel Trélat

Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes…

Robotics · Computer Science 2025-08-14 Hossein B. Jond

From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…

Optimization and Control · Mathematics 2014-03-24 Marco Caponigro , Massimo Fornasier , Benedetto Piccoli , Emmanuel Trélat

We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration and we apply them to analyze the emergence of collective behaviors. The Lohe type models have been proposed as possible non-abelian and…

Mathematical Physics · Physics 2021-02-03 Seung-Yeal Ha , Dohyun Kim , Hansol Park , Sang Woo Ryoo

Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…

Adaptation and Self-Organizing Systems · Physics 2018-10-03 Hui Wu , Mukesh Dhamala

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 consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…

Adaptation and Self-Organizing Systems · Physics 2011-11-16 Giambattista Giacomin , Eric Luçon , Christophe Poquet

Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two…

Adaptation and Self-Organizing Systems · Physics 2017-03-01 Hongjie Bi , Yan Li , Li Zhou , Shuguang Guan

Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave…

Adaptation and Self-Organizing Systems · Physics 2020-02-25 Joseph D. Johnson , Daniel M. Abrams

A generalization of the Cucker-Smale model for collective animal behaviour is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in…

Dynamical Systems · Mathematics 2015-07-17 Radek Erban , Jan Haskovec , Yongzheng Sun

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

All the fundamental interactions (such as gravity or electromagnetic interactions) are reciprocal in nature. However, in the macroscopic world, in particular outside equilibrium, non-reciprocal or non-mutual interactions are quite…

Statistical Mechanics · Physics 2025-11-26 Shaon Mandal Chakraborty , Bibhut Sahoo , Peter Sollich , Rituparno Mandal

Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 David Mertens

We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive…

Optimization and Control · Mathematics 2018-09-24 Rafael Bailo , Mattia Bongini , José A. Carrillo , Dante Kalise

We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. Using a geometric…

Mathematical Physics · Physics 2021-04-14 Stefan Achterhof , Janusz M Meylahn

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…

Adaptation and Self-Organizing Systems · Physics 2023-03-31 Jeremy Worsfold , Tim Rogers

We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between…

Adaptation and Self-Organizing Systems · Physics 2013-05-13 Maxim Komarov , Arkady Pikovsky

The collective motion of a finite nuclear system is investigated by numerical simulation and by linear response theory. Using a pseudo-particle simulation technique we analyze the giant resonances with a multipole decomposition scheme. We…

Nuclear Theory · Physics 2007-05-23 Klaus Morawetz , Uwe Fuhrmann , Rainer Walke

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…

Chaotic Dynamics · Physics 2015-05-20 Sergey P. Kuznetsov , Arkady Pikovsky , Michael Rosenblum