721 research outputs found
Array enhanced stochastic resonance and spatially correlated noises
We discuss the role of spatial correlations of the noise in the array
enhanced stochastic resonance. We show numerically that the noises with
negative correlations between different sites lead to significantly larger
values of the signal-to-noise ratio than the uncorrelated noises or noises with
positive correlations. If the noise is global, the system displays only the
conventional stochastic resonance, without any array enhancement.Comment: 6 pages in revTeX4, including 5 EPS figure
Population explosion suppressed by noise: Stationary distributions and how to simulate them
We show that two dynamical systems exhibiting very different deterministic
behaviours possess very similar stationary distributions when stabilized by a
multiplicative Gaussian white noise. We also discuss practical aspects of
numerically simulating these systems. We show that there exists a noise level
that is optimal in the sense that the interval during which discrete-time
versions of the systems remain physical is maximized. Analytical results are
illustrated by numerical examples.Comment: New Journal of Physics, submitte
Stationary distributions of a noisy logistic process
Stationary solutions to a Fokker-Planck equation corresponding to a noisy
logistic equation with correlated Gaussian white noises are constructed.
Stationary distributions exist even if the corresponding deterministic system
displays an unlimited growth. Positive correlations between the noises can lead
to a minimum of the variance of the process and to the stochastic resonance if
the system is additionally driven by a periodic signal.Comment: 15 pages in LaTeX incl. 4 PostScript figures. Submitted to Acta
Physica Polonica
The logistic equation and a linear stochastic resonance
We show analytically that a linear transmitter with correlated Gaussian white
noises displays a stochastic resonance. We discuss the relation of this problem
to a generalized noisy logistic equation.Comment: 13 pages and 3 EPS figures, submitted to Acta Phys. Pol.
Linear transmitter with correlated noises
A linear transmitter with correlated Gaussian white additive and
multiplicative noises and a periodic signal coupled either additively or
multiplicatively is considered. The correlations have a weak destructive effect
in case of the additive signal and a strong constructive effect in case of the
multiplicative one. Analytical results for the linear transmitter with the
additive signal agree with those obtained previously by a different approach.
We also show how to analytically calculate certain expectation values involving
exponentials of Gaussian processes.Comment: Physica A, accepted. Minor changes as compared to a previous versio
The Measurement of Time
We present a definition of time measurement based on high energy photons and
the fundamental length scale, and show that, for macroscopic time, it is in
accord with the Lorentz transformation of special relativity. To do this we
define observer in a different way than in special relativity.Comment: 8 pages, 4 figure
Microscopic Space Dimensions and the Discreteness of Time
We present a simple dynamical systems model for the effect of invisible space
dimensions on the visible ones. There are three premises. A: Orbits consist of
flows of probabilities [P].which is the case in the setting of quantum
mechanics. B: The orbits of probabilities are induced by (continuous time)
differential or partial differential equations. C: Observable orbit are flow of
marginal probabilities where the invisible space variables are averaged out. A
theorem is presented which proves that under certain general conditions the
transfer of marginal probabilities cannot be achieved by continuous time
dynamical systems acting on the space of observable variables but that it can
be achieved by discrete time dynamical systems.Comment: 8 page
noise in chemical reactions
A chemical system consisting of two species, one of which evolves
deterministically and independently of the other, which in turn is driven by
the dynamics of the former and by an additional multiplicative Gaussian white
noise, displays a noise for intermediate to large frequencies. A novel
mechanism responsible for the noise is suggested.Comment: 10 pages, RevTeX4, 3 PostScript figure
Chaos in Newtonian iterations: Searching for zeros which are not there
We show analytically that Newtonian iterations, when applied to a polynomial
equation, have a positive topological entropy. In a specific example of an
attempt to ``find'' the real solutions of the equation , we show that
the Newton method is chaotic. We analytically find the invariant density and
show how this problem relates to that of a piecewise linear map
Comment on ``Estimating scaling exponent from short time series"
A recently proposed method (O. Miramontes, P. Rohani, Physica D 166 (2002)
147) for estimating the scaling exponent in very short time series may give
wrong results, especially in case of undersampled data
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