Related papers: Time delay in the Kuramoto model with bimodal freq…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
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…
Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…
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…
Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a…
The production process of integrated electronic circuitry inherently leads to large heterogeneities on the component level. For electronic clock networks this implies detuned intrinsic frequencies and differences in coupling strength and…
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…
Motor coordination is an important feature of intra- and inter-personal interactions, and several scenarios --- from finger tapping to human-computer interfaces --- have been investigated experimentally. In the 1980, Haken, Kelso and Bunz…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic…
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…
We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…
We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to the Ornstein-Uhlenbeck (Gaussian) colored or the non-Gaussian colored noise. We investigate numerically the interplay…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function $f(\theta ) = \sin (\theta +\alpha _1) + h\sin 2(\theta +\alpha _2)$ is investigated based on the generalized…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…