222 research outputs found
Critical Phenomena and Diffusion in Complex Systems
Editorial of the International Conference on Critical Phenomena and Diffusion
in Complex Systems held on 5--7 December, 2006 in Nizhniy Novgorod State
University, Russia and was dedicated to the memory and 80th anniversary of
Professor Askold N. Malakhov.Comment: 4 pages, to appear in International Journal of Bifurcation and Chao
Noise Enhanced Stability
The noise can stabilize a fluctuating or a periodically driven metastable
state in such a way that the system remains in this state for a longer time
than in the absence of white noise. This is the noise enhanced stability
phenomenon, observed experimentally and numerically in different physical
systems. After shortly reviewing all the physical systems where the phenomenon
was observed, the theoretical approaches used to explain the effect are
presented. Specifically the conditions to observe the effect: (a) in systems
with periodical driving force, and (b) in random dichotomous driving force, are
discussed. In case (b) we review the analytical results concerning the mean
first passage time and the nonlinear relaxation time as a function of the white
noise intensity, the parameters of the potential barrier, and of the
dichotomous noise.Comment: 18 pages, 6 figures, in press Acta Physica Polonica (2004
Exact Results for Spectra of Overdamped Brownian Motion in Fixed and Randomly Switching Potentials
The exact formulae for spectra of equilibrium diffusion in a fixed bistable
piecewise linear potential and in a randomly flipping monostable potential are
derived. Our results are valid for arbitrary intensity of driving white
Gaussian noise and arbitrary parameters of potential profiles. We find: (i) an
exponentially rapid narrowing of the spectrum with increasing height of the
potential barrier, for fixed bistable potential; (ii) a nonlinear phenomenon,
which manifests in the narrowing of the spectrum with increasing mean rate of
flippings, and (iii) a nonmonotonic behaviour of the spectrum at zero
frequency, as a function of the mean rate of switchings, for randomly switching
potential. The last feature is a new characterization of resonant activation
phenomenon.Comment: in press in Acta Physica Polonica, vol. 35 (4), 200
Noise Enhanced Stability in Fluctuating Metastable States
We derive general equations for the nonlinear relaxation time of Brownian
diffusion in randomly switching potential with a sink. For piece-wise linear
dichotomously fluctuating potential with metastable state, we obtain the exact
average lifetime as a function of the potential parameters and the noise
intensity. Our result is valid for arbitrary white noise intensity and for
arbitrary fluctuation rate of the potential. We find noise enhanced stability
phenomenon in the system investigated: the average lifetime of the metastable
state is greater than the time obtained in the absence of additive white noise.
We obtain the parameter region of the fluctuating potential where the effect
can be observed. The system investigated also exhibits a maximum of the
lifetime as a function of the fluctuation rate of the potential.Comment: 7 pages, 5 figures, to appear in Phys. Rev. E vol. 69 (6),200
L\'evy flights versus L\'evy walks in bounded domains
L\'evy flights and L\'evy walks serve as two paradigms of random walks
resembling common features but also bearing fundamental differences. One of the
main dissimilarities are discontinuity versus continuity of their trajectories
and infinite versus finite propagation velocity. In consequence, well developed
theory of L\'evy flights is associated with their pathological physical
properties, which in turn are resolved by the concept of L\'evy walks. Here, we
explore L\'evy flights and L\'evy walks models on bounded domains examining
their differences and analogies. We investigate analytically and numerically
whether and under which conditions both approaches yield similar results in
terms of selected statistical observables characterizing the motion: the
survival probability, mean first passage time and stationary PDFs. It is
demonstrated that similarity of models is affected by the type of boundary
conditions and value of the stability index defining asymptotics of the jump
length distribution.Comment: 15 pages, 13 figure
Linear and nonlinear approximations for periodically driven bistable systems
We analyze periodically driven bistable systems by two different approaches. The first approach is a linearization of the stochastic Langevin equation of our system by the response on small external force. The second one is based on the Gaussian approximation of the kinetic equations for the cumulants. We obtain with the first approach the signal power amplification and output signal-to-noise ratio for a model piece-wise linear bistable potential and compare with the results of linear response approximation. By using the second approach to a bistable quartic potential, we obtain the set of nonlinear differential equations for the first and the second cumulants
New analytical approach to analyze the nonlinear regime of stochastic resonance
We propose some approximate methods to explore the nonlinear regime of the stochastic resonance phenomenon. These approximations correspond to different truncation schemes of cumulants. We compare the theoretical results for the signal power amplification, obtained by using ordinary cumulant truncation schemes, that is Gaussian and excess approximations, the modified two-state approximation with those obtained by numerical simulations of the Langevin equation describing the dynamics of the system
Enhancement of stability of metastable states in the presence of L\'{e}vy noise
The barrier crossing event for superdiffusion in the form of symmetric
L\'{e}vy flights is investigated. We derive from the fractional Fokker-Planck
equation a general differential equation with the corresponding conditions
useful to calculate the mean residence time of a particle in a fixed interval
for an arbitrary smooth potential profile, in particular metastable, with a
sink and a L\'{e}vy noise with an arbitrary index . A closed expression
in quadrature of the nonlinear relaxation time for L\'{e}vy flights with the
index in cubic metastable potential is obtained. Enhancement of the
mean residence time in the metastable state, analytically derived, due to
L\'{e}vy noise is found.Comment: 7 pages, 3 figure
Harmony perception and regularity of spike trains in a simple auditory model
A probabilistic approach for investigating the phenomena of dissonance and consonance
in a simple auditory sensory model, composed by two sensory neurons and one interneuron, is
presented. We calculated the interneuron’s firing statistics, that is the interspike interval statistics
of the spike train at the output of the interneuron, for consonant and dissonant inputs in the
presence of additional "noise", representing random signals from other, nearby neurons and from
the environment. We find that blurry interspike interval distributions (ISIDs) characterize dissonant
accords, while quite regular ISIDs characterize consonant accords. The informational entropy of the
non-Markov spike train at the output of the interneuron and its dependence on the frequency ratio of input sinusoidal signals is estimated. We introduce the regularity of spike train and suggested
the high or low regularity level of the auditory system’s spike trains as an indicator of feeling of
harmony during sound perception or disharmony, respectively
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