0000000000770646
AUTHOR
N. V. Agudov
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.
Stochastic model of memristor based on the length of conductive region
Abstract We propose a stochastic model of a voltage controlled bipolar memristive system, which includes the properties of widely used dynamic SPICE models and takes into account the fluctuations inherent in memristors. The proposed model is described by rather simple equations of Brownian diffusion, does not require significant computational resources for numerical modeling, and allows obtaining the exact analytical solutions in some cases. The noise-induced transient bimodality phenomenon, arising under resistive switching, was revealed and investigated theoretically and experimentally in a memristive system, by finding a quite good qualitatively agreement between theory and experiment. B…
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 …
Escape from a metastable state with fluctuating barrier
Abstract We investigate the escape of a Brownian particle from fluctuating metastable states. We find the conditions for the noise enhanced stability (NES) effect for periodical driving force. We obtain general equations useful to calculate the average escape time for randomly switching potential profiles. For piece-wise linear potential profile we reveal the noise enhanced stability (NES) effect, when the height of “reverse” potential barrier of metastable state is comparatively small. We obtain analytically the condition for the NES phenomenon and the average escape time as a function of parameters, which characterize the potential and the driving dichotomous noise.
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise enhanced stability (NES) phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential w…
Noise Enhanced Stability
The noise can stabilize a fluctuating or a periodically driven metastable state in such a way that the system remains in this state for a longer time than in the absence of white noise. This is the noise enhanced stability phenomenon, observed experimentally and numerically in different physical systems. After shortly reviewing all the physical systems where the phenomenon was observed, the theoretical approaches used to explain the effect are presented. Specifically the conditions to observe the effect: (a) in systems with periodical driving force, and (b) in random dichotomous driving force, are discussed. In case (b) we review the analytical results concerning the mean first passage time…
Stochastic resonance in a metal-oxide memristive device
Abstract The stochastic resonance phenomenon has been studied experimentally and theoretically for a state-of-art metal-oxide memristive device based on yttria-stabilized zirconium dioxide and tantalum pentoxide, which exhibits bipolar filamentary resistive switching of anionic type. The effect of white Gaussian noise superimposed on the sub-threshold sinusoidal driving signal is analyzed through the time series statistics of the resistive switching parameters, the spectral response to a periodic perturbation and the signal-to-noise ratio at the output of the nonlinear system. The stabilized resistive switching and the increased memristance response are revealed in the observed regularities…
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 mea…
Noise-enhanced stability of periodically driven metastable states
We study the effect of noise-enhanced stability of periodically driven metastable states in a system described by piecewise linear potential. We find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system. We analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations.
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 fluct…
Stochastic resonance in a trapping overdamped monostable system.
The response of a trapping overdamped monostable system to a harmonic perturbation is analyzed, in the context of stochastic resonance phenomenon. We consider the dynamics of a Brownian particle moving in a piecewise linear potential with a white Gaussian noise source. Based on linear-response theory and Laplace transform technique, analytical expressions of signal-to-noise ratio (SNR) and signal power amplification (SPA) are obtained. We find that the SNR is a nonmonotonic function of the noise intensity, while the SPA is monotonic. Theoretical results are compared with numerical simulations.
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 o…