Related papers: Frequency Spirals
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. This fascinating chimera state has until now been found only in non-local or globally coupled…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the…
A time dependent, complex scalar wavefield in three dimensions contains curved zero lines, wave 'vortices', that move around. From time to time pairs of these lines contact each other and 'reconnect' in a well studied manner, and at other…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
Twisted states with non-zero winding numbers composed of sinusoidally coupled identical oscillators have been observed in a ring. The phase of each oscillator in these states constantly shifts, following its preceding neighbor in a…
Over the past few decades, oscillating flexible foils have been used to study the physics of organismal propulsion in different fluid environments. Here we extend this work to a study of flexible foils in a frictional environment. When the…
Rotating spiral waves without phase singularity are found to arise in a certain class of three-component reaction-diffusion systems of biological relevance. It is argued that this phenomenon is universal when some chemical components…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane…
This contribution reports on numerical simulations of 2D granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibits spontaneous oscillatory motion in generic flow conditions, and…
Rotational states for trapped bosons in an optical lattice are studied in the framework of the Hubbard model. Critical frequencies are calculated and the main parameter regimes are identified. Transitions are observed from edge superfluids…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
We consider a two-dimensional wave system containing a subwavelength hole, such as an aperture in an interface supporting surface electromagnetic or acoustic waves, or an island in a fluid surface sustaining gravity-capillary waves. Recent…
We describe here an experimental technique based on the acoustic scattering phenomenon allowing the direct probing of the vorticity field in a turbulent flow. Using time-frequency distributions, recently introduced in signal analysis…
We study the dynamics of macroscopically-coherent matter waves of an ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites and demonstrate a novel type of spatio-temporal internal Josephson effect. Using a discrete…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
Spiral waves are observed in many natural phenomena. They have been extensively represented by the mathematical FitzHugh-Nagumo (FHN) model [Barkley et al., Phys. Rev. A 42, 2489 (1990)] of excitable media. In incompressible fluid…