12,331 research outputs found
Multifractal characterization of stochastic resonance
We use a multifractal formalism to study the effect of stochastic resonance
in a noisy bistable system driven by various input signals. To characterize the
response of a stochastic bistable system we introduce a new measure based on
the calculation of a singularity spectrum for a return time sequence. We use
wavelet transform modulus maxima method for the singularity spectrum
computations. It is shown that the degree of multifractality defined as a width
of singularity spectrum can be successfully used as a measure of complexity
both in the case of periodic and aperiodic (stochastic or chaotic) input
signals. We show that in the case of periodic driving force singularity
spectrum can change its structure qualitatively becoming monofractal in the
regime of stochastic synchronization. This fact allows us to consider the
degree of multifractality as a new measure of stochastic synchronization also.
Moreover, our calculations have shown that the effect of stochastic resonance
can be catched by this measure even from a very short return time sequence. We
use also the proposed approach to characterize the noise-enhanced dynamics of a
coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe
On the driven Frenkel-Kontorova model: II. Chaotic sliding and nonequilibrium melting and freezing
The dynamical behavior of a weakly damped harmonic chain in a spatially
periodic potential (Frenkel-Kontorova model) under the subject of an external
force is investigated. We show that the chain can be in a spatio-temporally
chaotic state called fluid-sliding state. This is proven by calculating
correlation functions and Lyapunov spectra. An effective temperature is
attributed to the fluid-sliding state. Even though the velocity fluctuations
are Gaussian distributed, the fluid-sliding state is clearly not in equilibrium
because the equipartition theorem is violated. We also study the transition
between frozen states (stationary solutions) and=7F molten states
(fluid-sliding states). The transition is similar to a first-order phase
transition, and it shows hysteresis. The depinning-pinning transition
(freezing) is a nucleation process. The frozen state contains usually two
domains of different particle densities. The pinning-depinning transition
(melting) is caused by saddle-node bifurcations of the stationary states. It
depends on the history. Melting is accompanied by precursors, called
micro-slips, which reconfigurate the chain locally. Even though we investigate
the dynamics at zero temperature, the behavior of the Frenkel-Kontorova model
is qualitatively similar to the behavior of similar models at nonzero
temperature.Comment: Written in RevTeX, 13 figures in PostScript, appears in PR
Fluctuation Relation beyond Linear Response Theory
The Fluctuation Relation (FR) is an asymptotic result on the distribution of
certain observables averaged over time intervals T as T goes to infinity and it
is a generalization of the fluctuation--dissipation theorem to far from
equilibrium systems in a steady state which reduces to the usual Green-Kubo
(GK) relation in the limit of small external non conservative forces. FR is a
theorem for smooth uniformly hyperbolic systems, and it is assumed to be true
in all dissipative ``chaotic enough'' systems in a steady state. In this paper
we develop a theory of finite time corrections to FR, needed to compare the
asymptotic prediction of FR with numerical observations, which necessarily
involve fluctuations of observables averaged over finite time intervals T. We
perform a numerical test of FR in two cases in which non Gaussian fluctuations
are observable while GK does not apply and we get a non trivial verification of
FR that is independent of and different from linear response theory. Our
results are compatible with the theory of finite time corrections to FR, while
FR would be observably violated, well within the precision of our experiments,
if such corrections were neglected.Comment: Version accepted for publication on the Journal of Statistical
Physics; minor changes; two references adde
Bistability and chaos at low-level of quanta
We study nonlinear phenomena of bistability and chaos at a level of few
quanta. For this purpose we consider a single-mode dissipative oscillator with
strong Kerr nonlinearity with respect to dissipation rate driven by a
monochromatic force as well as by a train of Gaussian pulses. The quantum
effects and decoherence in oscillatory mode are investigated on the framework
of the purity of states and the Wigner functions calculated from the master
equation. We demonstrate the quantum chaotic regime by means of a comparison
between the contour plots of the Wigner functions and the strange attractors on
the classical Poincar\'e section. Considering bistability at low-limit of
quanta, we analyze what is the minimal level of excitation numbers at which the
bistable regime of the system is displayed? We also discuss the formation of
oscillatory chaotic regime by varying oscillatory excitation numbers at ranges
of few quanta. We demonstrate quantum-interference phenomena that are assisted
hysteresis-cycle behavior and quantum chaos for the oscillator driven by the
train of Gaussian pulses as well as we establish the border of
classical-quantum correspondence for chaotic regimes in the case of strong
nonlinearities.Comment: 10 pages, 14 figure
Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks
How the information microscopically processed by individual neurons is
integrated and used in organizing the behavior of an animal is a central
question in neuroscience. The coherence of neuronal dynamics over different
scales has been suggested as a clue to the mechanisms underlying this
integration. Balanced excitation and inhibition may amplify microscopic
fluctuations to a macroscopic level, thus providing a mechanism for generating
coherent multiscale dynamics. Previous theories of brain dynamics, however,
were restricted to cases in which inhibition dominated excitation and
suppressed fluctuations in the macroscopic population activity. In the present
study, we investigate the dynamics of neuronal networks at a critical point
between excitation-dominant and inhibition-dominant states. In these networks,
the microscopic fluctuations are amplified by the strong excitation and
inhibition to drive the macroscopic dynamics, while the macroscopic dynamics
determine the statistics of the microscopic fluctuations. Developing a novel
type of mean-field theory applicable to this class of interscale interactions,
we show that the amplification mechanism generates spontaneous, irregular
macroscopic rhythms similar to those observed in the brain. Through the same
mechanism, microscopic inputs to a small number of neurons effectively entrain
the dynamics of the whole network. These network dynamics undergo a
probabilistic transition to a coherent state, as the magnitude of either the
balanced excitation and inhibition or the external inputs is increased. Our
mean-field theory successfully predicts the behavior of this model.
Furthermore, we numerically demonstrate that the coherent dynamics can be used
for state-dependent read-out of information from the network. These results
show a novel form of neuronal information processing that connects neuronal
dynamics on different scales.Comment: 20 pages 12 figures (main text) + 23 pages 6 figures (Appendix); Some
of the results have been removed in the revision in order to reduce the
volume. See the previous version for more result
Disorder Induced Diffusive Transport In Ratchets
The effects of quenched disorder on the overdamped motion of a driven
particle on a periodic, asymmetric potential is studied. While for the
unperturbed potential the transport is due to a regular drift, the quenched
disorder induces a significant additional chaotic ``diffusive'' motion. The
spatio-temporal evolution of the statistical ensemble is well described by a
Gaussian distribution, implying a chaotic transport in the presence of quenched
disorder.Comment: 10 pages, 4 EPS figures; submitted to Phys. Rev. Letter
Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence
The theoretical motivations to perform experimental tests of the stationary
state fluctuation relation are reviewed. The difficulties involved in such
tests, evidenced by numerical simulations, are also discussed.Comment: 36 pages, 4 figures. Extended version of a presentation to the
discussion "Is it possible to experimentally verify the fluctuation
theorem?", IHP, Paris, December 1, 2006. Comments are very welcom
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