Stochastic models of memristive behavior

TL;DR

This paper investigates how stochastic perturbations influence memristive devices under voltage drive, focusing on dynamic hysteresis and stochastic resonance. It analyzes two stochastic models: (i) an asymmetric double-well landscape producing dirty hysteresis and SR via barrier-crossing dynamics, and (ii) a harmonic (linear) or higher-order monostable well with correlated multiplicative and additive noises, yielding analytic SR conditions and variance minimization. The results show that noise can enhance current transduction and signal detection in memristive circuits, and that correlations between noise components can tune or suppress unwanted fluctuations. The work highlights connections between memristive memory and ion-channel gating, with implications for neuromorphic and bio-inspired information processing.

Abstract

Under normal operations, memristive devices undergo variability in time and space and have internal dynamics. Interplay of memory and stochastic signal processing in memristive devices makes them candidates for performing bio-inspired tasks of information transduction and transformation, where intrinsic random behavior can be harnessed for high performance of circuits built up of individual memory storing elements. The paper discusses models of single memristive devices exhibiting both - dynamic hysteresis and Stochastic Resonance, addressing also the cooperative effect of correlated noises acting on the system and occurrence of dirty hysteretic rounding.

Figures (9)

• Figure 1: Exemplary traces of a channel activity recorded at various conductance levels (C=closed state O=open state) and histograms of conducting states derived from them (presented at the right). Bottom: an asymmetric effective potential (free energy extracted from the stationary distribution) as $-k_BTl\ln(P(G))$
• Figure 2: Example trajectories (left column) and their corresponding hysteresis loops (right column) for the system \ref{['rownanie']}. Noise intensities are, top to bottom, $\sigma=0.01$, $\sigma=0.5$, and $\sigma=0.75$.
• Figure 3: The Signal-To-Noise Ratio in the system \ref{['rownanie']} as a function of the GWN intensity.
• Figure 4: Broken life --- the noisy hysteresis loop for $p=0.25$, $c=1$ and with the condition \ref{['resonance']} satisfied. The other parameters are $V_0=1$, $a=1$, $V_1=4$, $\omega=2\pi$. The colored line shows the clean hysteresis loop corresponding to the same set of parameters.
• Figure 5: Numerically obtained Signal-To-Noise ratio as a function of the intensity of the additive noise, $q$, for different values of the correlation coefficient, $c$ The multiplicative noise intensity $p=0.15$. All other parameters as in Fig. \ref{['petlaa']}.