Stochastic resonance: influence of a f-κ noise spectrum

With the aim of studying stochastic resonance (SR) in a double-well potential when the noise source has a spectral density of the form f^-κ (with varying κ), we have extended a procedure introduced by Kaulakys et al. (Phys. Rev. E 70, 020101 (2004)). In order to achieve an analytical understanding of the results, we have obtained an effective Markovian approximation that allows us to make a systematic study of the effect of such noise on the SR phenomenon. A comparison of the numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

A random walker on a ratchet potential: effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.     

Stochastic multiresonance in a bistable sawtooth potential driven by correlated multiplicative and additive noise

We present an analytic investigation of the signal-to-noise ratio (SNR) by studying the bistable sawtooth system driven by correlated Gaussian white noises. The analytic expression of SNR is obtained. Based on it, we detect the phenomenon of stochastic multiresonance, which arises from the dependence of SNR upon the noises correlation coefficient. Furthermore, there exists not only resonance, but also suppression in the SNR∼D (the additive noise intensity) curve and the SNR∼Q (the multiplicative noise intensity) curve. Received 26 February 2002 / Received in final form 12 July 2002 Published online 17 September 2002     

Exactly solvable reaction diffusion models on a Cayley tree

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.     

Modification of instability processes by multiplicative noises

We study two dynamical systems submitted to white and Gaussian random noise acting multiplicatively. The first system is an imperfect pitchfork bifurcation with a noisy departure from onset. The second system is a pitchfork bifurcation in which the noise acts multiplicatively on the non-linear term of lowest order. In both cases noise suppresses some solutions that exist in the deterministic regime. Besides, for the first system, the imperfectness of the bifurcation reduces the regime of on-off intermittency. For the second system, the unstable mode can achieve a jump of finite amplitude at instability but without hysteresis. We finally identify a generic property that is verified by the stationary probability density function of the dynamical variable when a control parameter is varied.     

Phase transition in annihilation-limited processes

A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of the average number of the particles tend to infinity, so that the annihilation rate times a certain power of the initial values of the average number of the particles remain constant (the double scaling) then if the initial state of the system is a multi-Poisson distribution, the system always remains in a state of multi-Poisson distribution, but with evolving parameters. The large time behavior of the system is also investigated. The system exhibits a dynamical phase transition. It is seen that for a k-particle annihilation, if k is larger than a critical value k_c, which is determined by the type-change rates, then annihilation does not enter the relaxation exponent of the system; while for k < k_c, it is the annihilation (in fact k itself) which determines the relaxation exponent.     

Multifractality of some random and disordered systems as a thermodynamics in fractal phase space

It is shown that multifractal properties of some random and disordered systems can be simulated using thermodynamics of a generalized ideal monoatomic gas in a fractal phase space. Received 25 November 1998 and Received in final form 16 December 1998     

Statistical equilibrium in simple exchange games I

This erratum corrects a mistake in reference [E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)]. In that paper, we needed an aperiodic version of the BDY game, but, in formula (1), we incorrectly presented a periodic transition matrix of period 2 in the special case of g = 2 agents. Here, we present the right aperiodic version.     

The underdamped Josephson junction subjected to colored noises

The properties of the underdamped Josephson junction subjected to colored noises were investigated with large and small phase difference (φ). For the case of the large φ, we found numerically that: (i) the probability distribution function of φ exhibits monostability → bistability → monostability transitions as the autocorrelation rate (λ) of a colored noise increases; (ii) in the bistability region the multiplicative noise drives the phase difference to turn over periodically; (iii) the slope K of the linear response of the junction potential difference (〈V 〉) can be somewhat reduced by means of tuning an optimal λ; (iv) the amplitude of φ in response to external sinusoidal signals changes with λ. For the case of small φ, after deriving the analytical expressions of the potential difference amplitude (〈V 〉_max) and the K in the presence of a dichotomous noise, we found nonmonotonic behavior of 〈V 〉_max and the slope K as a function of λ.     

A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small 1-r and large L, where r is the restitution coefficient and L the size of the container. We show that if the particle density n₀ and (1-r²)(n₀ Ld) where d is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, 〈E 〉/N, tends to a constant whereas the mean dissipated power per particle, 〈D 〉/N, decreases like when N increases, provided that (1-r²)(n₀ Ld)² < 1. The relative fluctuations of E, D and the power injected by the moving boundary, I, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power I(t) injected by the moving boundary.     

A multichannel shot noise approach to describe synaptic background activity in neurons

Systems driven by Poisson-distributed quantal inputs can be described as “shot noise” stochastic processes. This formalism can apply to neurons which receive a large number of Poisson-distributed synaptic inputs of similar quantal size. However, the presence of temporal correlations between these inputs destroys their quantal nature, and such systems can no longer be described by classical shot noise processes. Here, we show that explicit expressions for various statistical properties, such as the amplitude distribution and the power spectral density, can be deduced and investigated as functions of the correlation between input channels. The monotonic behavior of these expressions allows an one-to-one relation between temporal correlations and the statistics of fluctuations. Multi-channel shot noise processes, therefore, open a way to deduce correlations in input patterns by analyzing fluctuations in experimental systems. We discuss applications such as detecting correlations in networks of neurons from intracellular recordings of single neurons.     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Hypersensitivity to small signals in a stochastic system with multiplicative colored noise

Recently we discovered the phenomenon of hypersensitivity to small time-dependent signals in a simple stochastic system, the Kramers oscillator with multiplicative white noise. In the present work we study, theoretically and experimentally with analog simulations, an influence of noise correlation time on hypersensitivity in a nonlinear oscillator with piecewise-linear current-voltage characteristic and multiplicative colored dichotomous noise. We found that the region of hypersensitive behavior is defined by universal scaling index, whereas the specifics of a particular system reveals itself only in the dependence of the above index on system parameters. The dependence of gain factor on noise correlation time is of bell-shaped (resonant) type. Received 27 April 2000 and Received in final form 2 November 2000     

Bounding the quality of stochastic oscillations in population models

We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. Although usually defined a priori, the deterministic version of these models can be obtained as the infinite volume limit of many stochastic models (which are necessarily defined by more parameters than the deterministic one). It is known that damped oscillations in a deterministic model usually correspond to oscillatory-like fluctuations in their deterministic counterparts. The quality of these “oscillations" depends on details of each stochastic model. We show, however, that the parameters of the deterministic system are generally enough to obtain very good bounds for the quality of “oscillations" in any of its stochastic counterparts. These bounds are shown to depend on only one dimensionless parameter.     

Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.     

External fluctuations in front dynamics with inertia: The overdamped limit

We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative white noise arising from a control parameter of the system. Contrary to the non-inertial (overdamped) case, we find that important features of the system, such as the velocity selection picture, are not modified by the noise. We then compute the overdamped limit of the underdamped dynamics in a more careful way, finding that it does not exhibit any effect of noise either. Our result poses the question as to whether or not external noise sources can be measured in physical systems of this kind. Received 2 July 1999 and Received in final form 25 November 1999     

Coloured noise influence on system evolution

Within the power-law approach for noise amplitude dependence on stochastic variables, we present a picture of noise-induced transitions in systems affected by coloured multiplicative noise. The governed equations for main statistical moments are obtained and investigated in detail. We show that a reentrant noise-induced transition is realized within a window of the control parameter. Received 15 October 2001 / Received in final form 8 July 2002 Published online 17 September 2002