Related papers: Synchronization and Stability for Quantum Kuramoto
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematical approach offers analytical predictions for the linear…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
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 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…
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…
The Kuramoto--Sakaguchi model is a modification of the well-known Kuramoto model that adds a phase-lag paramater, or "frustration" to a network of phase-coupled oscillators. The Kuramoto model is a flow of gradient type, but adding a…
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…
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 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…
The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important…
Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…
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…
We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The…
We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…