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     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Adsorption of polymers anchored to membranes

Polymers, which are attached to a membrane at one of their ends, exert an entropic pressure, which curves the membrane away from the polymers. It is shown that adsorption which arises from a short-ranged potential between the polymer and the membrane has a large influence on the curvature of the membrane, leading to a decrease of the entropically induced curvature. If one ignores the finite size of the anchor segment, the polymer-induced curvature does not change sign and vanishes in the limit of strong adsorption and a pure contact potential. If one includes the finite size of the anchor segment, the membrane bends towards the polymer for sufficiently strong adsorption. Received 20 October 2000     

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics. Received 23 July 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

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.     

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.     

Properties of a growing random directed network

We study a number of properties of a simple random growing directed network which can be used to model real directed networks such as the world-wide web and call graphs. We confirm numerically that the distributions of in- and out-degree are consistent with a power law, in agreement with previous analytical results and with empirical measurements from real graphs. We study the distribution and mean of the minimum path length, the high degree nodes, the appearance and size of the giant component and the topology of the nodes outside the giant component. These properties are compared with empirical studies of the world-wide web. Received 15 June 2001 and Received in final form 12 July 2001     

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar. Received 28 March 2000     

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     

Learning, competition and cooperation in simple games

The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the number of strategies available to the agents increases, the collective gain made by the agents is reduced. This crowd effect arises from the fact that only a minority can profit at each moment, while all agents make their choices using the same input. We show that the properties of the model change drastically if the agents make choices based on their individual stories, keeping all remaining rules unaltered. This variation reduces the intrinsic frustration of the model, and improves the tendency towards cooperation and self organization. We finally study the stable mixing of individual and collective behavior. Received 30 June 1999 and Received in final form 27 September 1999     

Competition, efficiency and collective behavior in the “El Farol” bar model

The El Farol bar model, proposed to study the dynamics of competition of agents in a variety of contexts (W.B. Arthur, Amer. Econ. Assoc. Pap. Proc. 84, 406 (1994)) is studied. We characterize in detail the three regions of the phase diagram (efficient, better than random and inefficient) of the simplest version of the model (D. Challet, Y.-C. Zhang, Physica A 246, 407 (1997)). The efficient region is shown to have a rich structure, which is investigated in some detail. Changes in the payoff function enhance further the tendency of the model towards a wasteful distribution of resources. Received 13 November 1998     

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     

Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α < 2, the power law decay with large exponent ( α > 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement. Received 29 July 2000 and Received in final form 25 September 2000     

Random walks in one-dimensional environments with feedback-coupling

Random walks in one-dimensional environments with an additional dynamical feedback-coupling is analyzed numerically. The feedback introduced via a generalized master equation is controlled by a memory kernel of strength the explicit form of which is motivated by arguments used in mode-coupling theories. Introducing several realizations of the feedback mechanism within the simulations we obtain for a negative memory term, , superdiffusion in the long time limit while a positive memory leads to localization of the particle. The numerical simulations are in agreement with recent predictions based on renormalization group techniques. A slight modification of the model including an exponentially decaying memory term and some possible applications for glasses and supercooled liquids are suggested. The relation to the true self-avoiding is discussed. Received 16 September 1999 and Received in final form 27 December 1999     

Evolution of imitation networks in Minority Game model

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erd?s-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erd?s-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided.     

Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies E_c1 and E_c2 such that the resistivity decreases with N as a power law ∝ N ^{- γ} for electron energies within the range of [E _c1, E _c2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed. Received 18 December 2001 / Received in final form 2 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sjxiong@nju.edu.cn     

Distribution of return intervals of extreme events

The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values of the resistance fluctuations displayed by resistors with granular structure in nonequilibrium stationary states. The resistance fluctuations are calculated by Monte Carlo simulations using a resistor network approach. It has been found that for highly disordered networks, when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of return intervals of the extreme values is a stretched exponential, with exponent independent of the threshold.     

Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable “stochastic volatility” model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided. Received 22 May 2000