Related papers: Quantitative relaxation dynamics from generic init…
We study the collective behaviors of two second-order nonlinear consensus models with a bonding force, namely the Kuramoto model and the Cucker-Smale model with inter-particle bonding force. The proposed models contain feedback control…
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data…
We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading…
In this work, two-cluster modes are studied in a system of globally coupled Kuramoto-Sakaguchi phase oscillators with inertia. It is shown that these regimes can be of two types: with a constant intercluster phase difference rotating at the…
Recently it has been aroused a great interest about explosive (i.e., discontinuous) transitions. They manifest in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions and more…
We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the…
Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…
How higher-order interactions influence the dynamics of second order phase oscillators? We address this question using three coupled Kuramoto phase oscillators with inertia under both pairwise and higher order interactions, finding…
We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. We demonstrate that possible initial states of the condensate fall into two classes. In the first case, the order…
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…
Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto oscillators. We first establish a perturbation technique, by which universal normal forms and detailed dynamical behavior of this model can be…
The celebrated 1975 Kuramoto model of $N$ identical oscillators with phase angle vector $\boldsymbol{\vartheta}=(\vartheta_1,\ldots,\vartheta_N)$ and all-to-all coupling reads \begin{equation} \label{*}…
Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble…
We present and analyze a nonabelian version of the Kuramoto system, which we call the quantum Kuramoto system. We study the stability of several classes of special solutions to this system, and show that for certain connection topologies…
We report the appearance of a scroll ring and scroll toroid chimera states from the proposed initial conditions for the Kuramoto model of coupled phase oscillators in the 3D grid topology with inertia. The proposed initial conditions…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…
We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
We numerically study the relaxation dynamics of impurity-host systems, focusing on the presence of long-lived metastable states in the non-equilibrium dynamics after an initial excitation of the impurities. In generic systems, an excited…