Related papers: Exact Response Theory and Kuramoto dynamics
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…
A general exact theory of autoresonance (self-sustained resonance) in both dissipative and Hamiltonian nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the…
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $\mathbf{S}^{1}$, driven…
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…
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…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
We consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large…
The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model.…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
Networks of coupled oscillators are some of the most studied objects in the theory of dynamical systems. Two important areas of current interest are the study of synchrony in highly disordered systems and the modeling of systems with…
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…
For the Kuramoto model and its variations, it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry. %due to the asymmetry of the adjacency matrices. In this paper, for the…
We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…
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…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…
The Kuramoto model is a paradigmatic model of collective synchronization in coupled oscillator systems. Although its mathematical properties have been extensively investigated, exact phase trajectories from arbitrary initial conditions have…
The circadian oscillator exhibits remarkably high temporal precision, despite its exposure to several fluctuations. The central mechanism that protects the oscillator from fluctuations is a collective enhancement of precision, where a…