Related papers: On Synchronization of Coupled Hopf-Kuramoto Oscill…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a…
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 investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as…
We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…
We discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on time delay in terms of initial…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
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…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
We study the collective dynamics of coupled Stuart--Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems,…
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…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…