Related papers: Frequency Spirals
Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to…
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,…
A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales [1]. These patterns both arise as secondary states once the primary…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
We present an experimental study of the statistical properties of millimeter-size spheres floating on the surface of a turbulent flow. The flow is generated in a layer of liquid metal by an electromagnetic forcing. By using two magnet…
We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio…
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
A semiclassical model is used to investigate oscillations of atomic fermions in a combined magnetic trap and one dimensional optical lattice potential following axial displacement of the trap. The oscillations are shown to have a…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in…
The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where particles were characterized by a single phase. In this setup,…
We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits with a variety of different periods, which can be orders of magnitude longer…
We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating…
Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…