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

1/f1/f 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 $1/f$ noise for intermediate to large frequencies. A novel mechanism responsible for the $1/f$ 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 $x^2+1=0$, 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 1/fα1/f^\alpha 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