Related papers: Kuramoto model on the $D$-dimensional torus
We consider the mean-field noisy Kuramoto-Daido model, which is a McKean-Vlasov equation on the circle with bimodal interaction $W(\theta)=\cos\theta+m\cos2\theta$ for $m\ge 0$ and interaction strength $K$, generalizing the celebrated noisy…
The synchronization phenomena in thermoacoustic systems leading to oscillatory instability can effectively be modeled using Kuramoto oscillators. Such models consider the nonlinear response of flame as an ensemble of Kuramoto phase…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We construct a nontrivial generalization of the paradigmatic Kuramoto model by using an additional coupling term that explicitly breaks its rotational symmetry resulting in a variant of the Winfree Model. Consequently, we observe the…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
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…
In a system of heterogeneous (Abelian) Kuramoto oscillators with random or `frustrated' interactions, transitions from states of incoherence to partial synchronization were observed. These so-called volcano transitions are characterized by…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
Chimera dynamics is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase…
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…
A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show…
We consider a recently introduced $D$-dimensional generalized Kuramoto model for many $(N\gg 1)$ interacting agents in which the agent states are $D$-dimensional unit vectors. It was previously shown that, for even $D$, similar to the…
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,…
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…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…
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…
Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivial stochastic dynamics. Each isolated system is a diffusion…
We study the bifurcations and phase diagram for a network of identical Kuramoto oscillators with a coupling that explicitly breaks the rotational symmetry of the equations. Applying the Watanabe-Strogatz ansatz, the original N-dimensional…