1,388 research outputs found
Chimera and globally clustered chimera: Impact of time delay
Following a short report of our preliminary results [Phys. Rev. E 79,
055203(R) (2009)], we present a more detailed study of the effects of coupling
delay in diffusively coupled phase oscillator populations. We find that
coupling delay induces chimera and globally clustered chimera (GCC) states in
delay coupled populations. We show the existence of multi-clustered states that
act as link between the chimera and the GCC states. A stable GCC state goes
through a variety of GCC states, namely periodic, aperiodic, long-- and
short--period breathers and becomes unstable GCC leading to global
synchronization in the system, on increasing time delay. We provide numerical
evidence and theoretical explanations for the above results and discuss
possible applications of the observed phenomena.Comment: 10 pages, 10 figures, Accepted in Phys. Rev.
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
Globally clustered chimera states in delay--coupled populations
We have identified the existence of globally clustered chimera states in
delay coupled oscillator populations and find that these states can breathe
periodically, aperiodically and become unstable depending upon the value of
coupling delay. We also find that the coupling delay induces frequency
suppression in the desynchronized group. We provide numerical evidence and
theoretical explanations for the above results and discuss possible
applications of the observed phenomena.Comment: Accepted in Phys. Rev. E as a Rapid Communicatio
Dynamics of the Singlet-Triplet System Coupled with Conduction Spins -- Application to Pr Skutterudites
Dynamics of the singlet-triplet crystalline electric field (CEF) system at
finite temperatures is discussed by use of the non-crossing approximation. Even
though the Kondo temperature is smaller than excitation energy to the CEF
triplet, the Kondo effect appears at temperatures higher than the CEF
splitting, and accordingly only quasi-elastic peak is found in the magnetic
spectra. On the other hand, at lower temperatures the CEF splitting suppresses
the Kondo effect and inelastic peak develops. The broad quasi-elastic neutron
scattering spectra observed in PrFe_4P_{12} at temperatures higher than the
quadrupole order correspond to the parameter range where the CEF splittings are
unimportant.Comment: 16 pages, 12 figures, 1 tabl
Heterogeneity Induced Order in Globally Coupled Chaotic Systems
Collective behavior is studied in globally coupled maps with distributed
nonlinearity. It is shown that the heterogeneity enhances regularity in the
collective dynamics. Low-dimensional quasiperiodic motion is often found for
the mean-field, even if each element shows chaotic dynamics. The mechanism of
this order is due to the formation of an internal bifurcation structure, and
the self-consistent dynamics between the structures and the mean-field.
Keywords: Globally Coupled Map with heterogeneity, Collective behaviorComment: 11 pages (Revtex) + 4 figures (PostScript,tar+gzip
A new approach to partial synchronization in globally coupled rotators
We develop a formalism to analyze the behaviour of pulse--coupled identical
phase oscillators with a specific attention devoted to the onset of partial
synchronization. The method, which allows describing the dynamics both at the
microscopic and macroscopic level, is introduced in a general context, but then
the application to the dynamics of leaky integrate-and-fire (LIF) neurons is
analysed. As a result, we derive a set of delayed equations describing exactly
the LIF behaviour in the thermodynamic limit. We also investigate the weak
coupling regime by means of a perturbative analysis, which reveals that the
evolution rule reduces to a set of ordinary differential equations. Robustness
and generality of the partial synchronization regime is finally tested both by
adding noise and considering different force fields.Comment: 5 pages, 3 eps figure
Excitonic Bound State in the Extended Anderson Model with c-f Coulomb Interaction
The Anderson model with the Coulomb interaction between the local and
conduction electrons is studied in the semiconducting phase. Based on a
perturbation theory from the atomic limit, leading contributions for the c-f
Coulomb interaction are incorporated as a vertex correction to hybridization.
An analytical solution shows that the effective attraction in the intermediate
states leads to a bound state localized at the local electron site.
Self-consistent equations are constructed as an extension of the non-crossing
approximation (NCA) to include the vertex part yielding the bound state. A
numerical calculation demonstrates the excitonic bound state inside the
semiconducting gap for single-particle excitations, and a discontinuity at the
gap edge for magnetic excitations.Comment: 15 pages, 20 figures, submitted to J. Phys. Soc. Jp
Phase reduction of stochastic limit cycle oscillators
We point out that the phase reduction of stochastic limit cycle oscillators
has been done incorrectly in the literature. We present a correct phase
reduction method for oscillators driven by weak external white Gaussian noises.
Numerical evidence demonstrates that the present phase equation properly
approximates the dynamics of the original full oscillator system.Comment: 4 pages, 2 figure
Dynamics of Limit Cycle Oscillator Subject to General Noise
The phase description is a powerful tool for analyzing noisy limit cycle
oscillators. The method, however, has found only limited applications so far,
because the present theory is applicable only to the Gaussian noise while noise
in the real world often has non-Gaussian statistics. Here, we provide the phase
reduction for limit cycle oscillators subject to general, colored and
non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like
mean frequency, diffusion constant, and the Lyapunov exponent to confirm
consistency of the result. Applying our results, we additionally study a
resonance between the phase and noise.Comment: main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the
document, 1 figur
Synchronization in a System of Globally Coupled Oscillators with Time Delay
We study the synchronization phenomena in a system of globally coupled
oscillators with time delay in the coupling. The self-consistency equations for
the order parameter are derived, which depend explicitly on the amount of
delay. Analysis of these equations reveals that the system in general exhibits
discontinuous transitions in addition to the usual continuous transition,
between the incoherent state and a multitude of coherent states with different
synchronization frequencies. In particular, the phase diagram is obtained on
the plane of the coupling strength and the delay time, and ubiquity of
multistability as well as suppression of the synchronization frequency is
manifested. Numerical simulations are also performed to give consistent
results
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