Related papers: Generalized coupling in the Kuramoto model
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…
The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…
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…
Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the…
We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is…
This article investigates the Kuramoto model with three oscillators that are interconnected by an isosceles triangle network. The characteristic of this model is that the coupling connections between the oscillators can be either attractive…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
We study the onset of synchronization in square lattices of limit cycle oscillators with long-range coupling by means of numerical simulations of the Kuramoto model. In this regime the critical coupling strength depends on the system size…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
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…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are…
The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external…
Quantum fluctuations of the phases of the order parameter in 2D arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…
We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…