Noise delayed decay of unstable states: theory versus numerical simulations

We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for polynomial potential profiles and obtain nonmonotonic behavior of the decay times as a function of the noise intensity for the unstable nonequilibrium states. The analytical results are compared with numerical simulations.Comment: 9 pages, 6 figures, in press in J. Phys.

Enhancement of stability in randomly switching potential with metastable state

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviours as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.Comment: 9 pages, 5 figures. In press in "European Physical Journal B

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

Volatility Effects on the Escape Time in Financial Market Models

We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.Comment: 12 pages, 9 figures, to appear in Int. J. of Bifurcation and Chaos, 200

Field- and irradiation-induced phenomena in memristive nanomaterials

The breakthrough in electronics and information technology is anticipated by the development of emerging memory and logic devices, artificial neural networks and brain-inspired systems on the basis of memristive nano-materials represented, in a particular case, by a simple 'metal-insulator-metal' (MIM) thin-film structure. The present article is focused on the comparative analysis of MIM devices based on oxides with dominating ionic (ZrOx, HfOx) and covalent (SiOx, GeOx) bonding of various composition and geometry deposited by magnetron sputtering. The studied memristive devices demonstrate reproducible change in their resistance (resistive switching - RS) originated from the formation and rupture of conductive pathways (filaments) in oxide films due to the electric-field-driven migration of oxygen vacancies and/or mobile oxygen ions. It is shown that, for both ionic and covalent oxides under study, the RS behaviour depends only weakly on the oxide film composition and thickness, device geometry (down to a device size of about 20x20 mu m(2)). The devices under study are found to be tolerant to ion irradiation that reproduces the effect of extreme fluences of high-energy protons and fast neutrons. This common behaviour of RS is explained by the localized nature of the redox processes in a nanoscale switching oxide volume. Adaptive (synaptic) change of resistive states of memristive devices is demonstrated under the action of single or repeated electrical pulses, as well as in a simple model of coupled (synchronized) neuron-like generators. It is concluded that the noise-induced phenomena cannot be neglected in the consideration of a memristive device as a nonlinear system. The dynamic response of a memristive device to periodic signals of complex waveform can be predicted and tailored from the viewpoint of stochastic resonance concept. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

Ecological Complex Systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noises role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.Comment: 13 pages, Editorial of a topical issue on Ecological Complex System to appear in EPJ B, Vol. 65 (2008

Gaussian models for the distribution of Brownian particles in tilted periodic potentials

We present two Gaussian approximations for the time-dependent probability density function (PDF) of an overdamped Brownian particle moving in a tilted periodic potential. We assume high potential barriers in comparison with the noise intensity. The accuracy of the proposed approximated expressions for the time-dependent PDF is checked with numerical simulations of the Langevin dynamics. We found a quite good agreement between theoretical and numerical results at all times

Nonstationary distributions and relaxation times in a stochastic model of memristor

We propose a stochastic model for a memristive system by generalizing known approaches and experimental results. We validate our theoretical model by experiments carried out on a memristive device based on multilayer structure. In the framework of the proposed model we obtain the exact analytic expressions for stationary and nonstationary solutions. We analyze the equilibrium and non-equilibrium steady-state distributions of the internal state variable of the memristive system and study the influence of fluctuations on the resistive switching, including the relaxation time to the steady-state. The relaxation time shows a nonmonotonic dependence, with a minimum, on the intensity of the fluctuations. This paves the way for using the intensity of fluctuations as a control parameter for switching dynamics in memristive devices