1,514 research outputs found
An experimental route to spatiotemporal chaos in an extended 1D oscillators array
We report experimental evidence of the route to spatiotemporal chaos in a
large 1D-array of hotspots in a thermoconvective system. Increasing the driving
force, a stationary cellular pattern becomes unstable towards a mixed pattern
of irregular clusters which consist of time-dependent localized patterns of
variable spatiotemporal coherence. These irregular clusters coexist with the
basic cellular pattern. The Fourier spectra corresponding to this
synchronization transition reveals the weak coupling of a resonant triad. This
pattern saturates with the formation of a unique domain of great spatiotemporal
coherence. As we further increase the driving force, a supercritical
bifurcation to a spatiotemporal beating regime takes place. The new pattern is
characterized by the presence of two stationary clusters with a characteristic
zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables
to find out that this beating phenomena is produced by the splitting of the
fundamental spatiotemporal frequencies in a narrow band. Both secondary
instabilities are phase-like synchronization transitions with global and
absolute character. Far beyond this threshold, a new instability takes place
when the system is not able to sustain the spatial frequency splitting,
although the temporal beating remains inside these domains. These experimental
results may support the understanding of other systems in nature undergoing
similar clustering processes.Comment: 12 pages, 13 figure
Chimera States for Coupled Oscillators
Arrays of identical oscillators can display a remarkable spatiotemporal
pattern in which phase-locked oscillators coexist with drifting ones.
Discovered two years ago, such "chimera states" are believed to be impossible
for locally or globally coupled systems; they are peculiar to the intermediate
case of nonlocal coupling. Here we present an exact solution for this state,
for a ring of phase oscillators coupled by a cosine kernel. We show that the
stable chimera state bifurcates from a spatially modulated drift state, and
dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure
Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
We study collective behavior of locally coupled limit-cycle oscillators with
random intrinsic frequencies, spatially extended over -dimensional
hypercubic lattices. Phase synchronization as well as frequency entrainment are
explored analytically in the linear (strong-coupling) regime and numerically in
the nonlinear (weak-coupling) regime. Our analysis shows that the oscillator
phases are always desynchronized up to , which implies the lower critical
dimension for phase synchronization. On the other hand, the
oscillators behave collectively in frequency (phase velocity) even in three
dimensions (), indicating that the lower critical dimension for frequency
entrainment is . Nonlinear effects due to periodic nature of
limit-cycle oscillators are found to become significant in the weak-coupling
regime: So-called {\em runaway oscillators} destroy the synchronized (ordered)
phase and there emerges a fully random (disordered) phase. Critical behavior
near the synchronization transition into the fully random phase is unveiled via
numerical investigation. Collective behavior of globally-coupled oscillators is
also examined and compared with that of locally coupled oscillators.Comment: 18 pages, 18 figure
A power-law distribution of phase-locking intervals does not imply critical interaction
Neural synchronisation plays a critical role in information processing,
storage and transmission. Characterising the pattern of synchronisation is
therefore of great interest. It has recently been suggested that the brain
displays broadband criticality based on two measures of synchronisation - phase
locking intervals and global lability of synchronisation - showing power law
statistics at the critical threshold in a classical model of synchronisation.
In this paper, we provide evidence that, within the limits of the model
selection approach used to ascertain the presence of power law statistics, the
pooling of pairwise phase-locking intervals from a non-critically interacting
system can produce a distribution that is similarly assessed as being power
law. In contrast, the global lability of synchronisation measure is shown to
better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits
throughout. Clarified relationship between theoretical critical coupling for
infinite size system and 'effective' critical coupling system for finite size
system. Improved presentation and discussion of results; results unchanged.
Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11
pages, 7 figure
Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators
We study the existence and stability of phaselocked patterns and amplitude
death states in a closed chain of delay coupled identical limit cycle
oscillators that are near a supercritical Hopf bifurcation. The coupling is
limited to nearest neighbors and is linear. We analyze a model set of discrete
dynamical equations using the method of plane waves. The resultant dispersion
relation, which is valid for any arbitrary number of oscillators, displays
important differences from similar relations obtained from continuum models. We
discuss the general characteristics of the equilibrium states including their
dependencies on various system parameters. We next carry out a detailed linear
stability investigation of these states in order to delineate their actual
existence regions and to determine their parametric dependence on time delay.
Time delay is found to expand the range of possible phaselocked patterns and to
contribute favorably toward their stability. The amplitude death state is
studied in the parameter space of time delay and coupling strength. It is shown
that death island regions can exist for any number of oscillators N in the
presence of finite time delay. A particularly interesting result is that the
size of an island is independent of N when N is even but is a decreasing
function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from
TeX); minor additions; typos correcte
Kuramoto model with coupling through an external medium
Synchronization of coupled oscillators is often described using the Kuramoto
model. Here we study a generalization of the Kuramoto model where oscillators
communicate with each other through an external medium. This generalized model
exhibits interesting new phenomena such as bistability between synchronization
and incoherence and a qualitatively new form of synchronization where the
external medium exhibits small-amplitude oscillations. We conclude by
discussing the relationship of the model to other variations of the Kuramoto
model including the Kuramoto model with a bimodal frequency distribution and
the Millennium Bridge problem.Comment: 9 pages, 3 figure
Negative refraction in nonlinear wave systems
People have been familiar with the phenomenon of wave refraction for several
centuries. Recently, a novel type of refraction, i.e., negative refraction,
where both incident and refractory lines locate on the same side of the normal
line, has been predicted and realized in the context of linear optics in the
presence of both right- and left-handed materials. In this work, we reveal, by
theoretical prediction and numerical verification, negative refraction in
nonlinear oscillatory systems. We demonstrate that unlike what happens in
linear optics, negative refraction of nonlinear waves does not depend on the
presence of the special left-handed material, but depends on suitable physical
condition. Namely, this phenomenon can be observed in wide range of oscillatory
media under the Hopf bifurcation condition. The complex Ginzburg-Landau
equation and a chemical reaction-diffusion model are used to demonstrate the
feasibility of this nonlinear negative refraction behavior in practice
Coarse-graining the dynamics of coupled oscillators
We present an equation-free computational approach to the study of the
coarse-grained dynamics of {\it finite} assemblies of {\it non-identical}
coupled oscillators at and near full synchronization. We use coarse-grained
observables which account for the (rapidly developing) correlations between
phase angles and oscillator natural frequencies. Exploiting short bursts of
appropriately initialized detailed simulations, we circumvent the derivation of
closures for the long-term dynamics of the assembly statistics.Comment: accepted for publication in Phys. Rev. Let
Extracting topological features from dynamical measures in networks of Kuramoto oscillators
The Kuramoto model for an ensemble of coupled oscillators provides a
paradigmatic example of non-equilibrium transitions between an incoherent and a
synchronized state. Here we analyze populations of almost identical oscillators
in arbitrary interaction networks. Our aim is to extract topological features
of the connectivity pattern from purely dynamical measures, based on the fact
that in a heterogeneous network the global dynamics is not only affected by the
distribution of the natural frequencies, but also by the location of the
different values. In order to perform a quantitative study we focused on a very
simple frequency distribution considering that all the frequencies are equal
but one, that of the pacemaker node. We then analyze the dynamical behavior of
the system at the transition point and slightly above it, as well as very far
from the critical point, when it is in a highly incoherent state. The gathered
topological information ranges from local features, such as the single node
connectivity, to the hierarchical structure of functional clusters, and even to
the entire adjacency matrix.Comment: 11 pages, 10 figure
Soliton turbulences in the complex Ginzburg-Landau equation
We study spatio-temporal chaos in the complex Ginzburg-Landau equation in
parameter regions of weak amplification and viscosity. Turbulent states
involving many soliton-like pulses appear in the parameter range, because the
complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger
equation. We find that the distributions of amplitude and wavenumber of pulses
depend only on the ratio of the two parameters of the amplification and the
viscosity. This implies that a one-parameter family of soliton turbulence
states characterized by different distributions of the soliton parameters
exists continuously around the completely integrable system.Comment: 5 figure
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