Related papers: Phase Synchronization and Polarization Ordering of…
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a…
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation…
Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…
A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we…
We consider $N$ oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength $\kappa$ and the spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled…
Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be…
The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an…
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…
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…
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
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…
The problem of synchronization of coupled self-oscillators by external force is studied. The charts of Lyapunov's exponents in the "frequency - amplitude" parameter plane are obtained within the framework of the phase approximation. We…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
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 introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate 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…
In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling…
The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…