1,924 research outputs found
Chemical turbulence equivalent to Nikolavskii turbulence
We find evidence that a certain class of reaction-diffusion systems can
exhibit chemical turbulence equivalent to Nikolaevskii turbulence. The
distinctive characteristic of this type of turbulence is that it results from
the interaction of weakly stable long-wavelength modes and unstable
short-wavelength modes. We indirectly study this class of reaction-diffusion
systems by considering an extended complex Ginzburg-Landau (CGL) equation that
was previously derived from this class of reaction-diffusion systems. First, we
show numerically that the power spectrum of this CGL equation in a particular
regime is qualitatively quite similar to that of the Nikolaevskii equation.
Then, we demonstrate that the Nikolaevskii equation can in fact be obtained
from this CGL equation through a phase reduction procedure applied in the
neighborhood of a codimension-two Turing--Benjamin-Feir point.Comment: 10 pages, 3 figure
Chimera Ising Walls in Forced Nonlocally Coupled Oscillators
Nonlocally coupled oscillator systems can exhibit an exotic spatiotemporal
structure called chimera, where the system splits into two groups of
oscillators with sharp boundaries, one of which is phase-locked and the other
is phase-randomized. Two examples of the chimera states are known: the first
one appears in a ring of phase oscillators, and the second one is associated
with the two-dimensional rotating spiral waves. In this article, we report yet
another example of the chimera state that is associated with the so-called
Ising walls in one-dimensional spatially extended systems, which is exhibited
by a nonlocally coupled complex Ginzburg-Landau equation with external forcing.Comment: 7 pages, 5 figures, to appear in Phys. Rev.
Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
The onset of synchronization in networks of networks is investigated.
Specifically, we consider networks of interacting phase oscillators in which
the set of oscillators is composed of several distinct populations. The
oscillators in a given population are heterogeneous in that their natural
frequencies are drawn from a given distribution, and each population has its
own such distribution. The coupling among the oscillators is global, however,
we permit the coupling strengths between the members of different populations
to be separately specified. We determine the critical condition for the onset
of coherent collective behavior, and develop the illustrative case in which the
oscillator frequencies are drawn from a set of (possibly different)
Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in
which the collective dynamics of several interacting populations of oscillators
(such as excitatory and inhibitory neurons and glia) are of interest.Comment: The original was replaced with a version that has been accepted to
Phys. Rev. E. The new version has the same content, but the title, abstract,
and the introductory text have been revise
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
Hole Structures in Nonlocally Coupled Noisy Phase Oscillators
We demonstrate that a system of nonlocally coupled noisy phase oscillators
can collectively exhibit a hole structure, which manifests itself in the
spatial phase distribution of the oscillators. The phase model is described by
a nonlinear Fokker-Planck equation, which can be reduced to the complex
Ginzburg-Landau equation near the Hopf bifurcation point of the uniform
solution. By numerical simulations, we show that the hole structure clearly
appears in the space-dependent order parameter, which corresponds to the
Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
Collective Phase Sensitivity
The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.Comment: 6 pages, 3 figure
Multistable attractors in a network of phase oscillators with three-body interaction
Three-body interactions have been found in physics, biology, and sociology.
To investigate their effect on dynamical systems, as a first step, we study
numerically and theoretically a system of phase oscillators with three-body
interaction. As a result, an infinite number of multistable synchronized states
appear above a critical coupling strength, while a stable incoherent state
always exists for any coupling strength. Owing to the infinite multistability,
the degree of synchrony in asymptotic state can vary continuously within some
range depending on the initial phase pattern.Comment: 5 pages, 3 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
Entrainment transition in populations of random frequency oscillators
The entrainment transition of coupled random frequency oscillators is
revisited. The Kuramoto model (global coupling) is shown to exhibit unusual
sample-dependent finite size effects leading to a correlation size exponent
. Simulations of locally coupled oscillators in -dimensions
reveal two types of frequency entrainment: mean-field behavior at , and
aggregation of compact synchronized domains in three and four dimensions. In
the latter case, scaling arguments yield a correlation length exponent
, in good agreement with numerical results.Comment: published versio
Paths to Synchronization on Complex Networks
The understanding of emergent collective phenomena in natural and social
systems has driven the interest of scientists from different disciplines during
decades. Among these phenomena, the synchronization of a set of interacting
individuals or units has been intensively studied because of its ubiquity in
the natural world. In this paper, we show how for fixed coupling strengths
local patterns of synchronization emerge differently in homogeneous and
heterogeneous complex networks, driving the process towards a certain global
synchronization degree following different paths. The dependence of the
dynamics on the coupling strength and on the topology is unveiled. This study
provides a new perspective and tools to understand this emerging phenomena.Comment: Final version published in Physical Review Letter
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