Generalized boundary condition memristor model

Abstract

SUMMARYA number of resistive switching memories exhibit activation-based dynamical behavior, which makes them suitable for neuromorphic and programmable analog filtering applications. Because the Boundary Condition Memristor (BCM) model accounts for tunable activation thresholds only at the on and off boundary states, it is not quantitatively accurate in the description of these kinds of memristors and in the investigation of their circuit applications. This paper introduces the Generalized Boundary Condition Memristor (GBCM) model, preserving the features of the BCM model while allowing, further, an ad-hoc tuning of activation-based dynamics, which enables an appropriate modulation of the conditions under which memristors may operate as storage elements or data processors. A simple circuit implementation of the novel model is presented, and time-efficient simulations confirming the improvement in modeling accuracy over the BCM model are shown. As a proof-of-concept for the suitability of the GBCM model in the exploration of the full potential of memristors in neuromorphic circuits and programmable analog filters, this paper adopts it to model fundamental synaptic rules governing the mechanisms of learning in neural systems and to gain some insight into key issues in the design of a couple of filters.

Robust Simulation of a TaO Memristor Model

“…As a result, the replacement of discontinuous and piecewise differentiable functions with appropriate continuous and differentiable approximations may facilitate the numerical integration of the models. With reference to the modelling equations of the HP TaO memristor, it is evident that two are the functions under our zooming lens, particularly the discontinuous step function in the state equation (13), and the piecewise differentiable modulus function in the memductance function (see (15)) appearing in the Ohm's based law (14). The modulus function, acting on the memristor voltage v m and denoted as |v m | in (15), may be replaced by differentiable approximations falling into the following class:…”

“…The state equation (13) is modelled by the charging rate of this capacitor driven by yet another voltage-dependent current source G Y placed in parallel to it. This current source, controlled by the same voltage inputs as G res , defines the current flowing through the capacitor, which is specified by the memristor state evolution function, reported on the right hand side of (13). A large auxiliary resistance R aux is also inserted in parallel to the capacitor to prevent convergence issues in the circuit simulator.…”

“…In fact the history-dependent conductance of the memristor may mimic the plasticity of the synaptic weight, which is finely tuned upon changes in the ionic flow through the synapse. Memristors may support various synaptic rules at the origin of neural learning, including habituation, long-term potentiation (LTP) [12], Hebb's and anti-Hebb's rules [13], spike-timing-dependent-plasticity [14]- [15] (based on either pairs or triplets of spikes), and even spike-rate-dependent-plasticity. The availability of CMOS circuits for the emulation of neurons, and the possibility to stack over them multiple layers of memristor arrays, may lead to the development of a bio-inspired computing engine with massively-parallel signal processing power, capable to reproduce the complex dynamics of the neural networks of the human brain.…”

Memristor for Neuromorphic Applications: Models and Circuit Implementations

“…It is noteworthy that the class of detectable dynamics include not only all the behaviors observed in the HP memristor [3], but also phenomena exhibited by various other nano-structures where memristor behavior arises from distinct physical mechanisms [17][18][19][20]. In order to enable the BCM model to support various neural learning rules, we recently developed a generalized version [21], in which the activation threshold property characterizing the boundary behavior in the original BCM model [12] is extended to the whole admissible range of the state variable, thus allowing the modeling of the degree of non-volatility of the nano-device.…”

Reliable Modeling of Ideal Generic Memristors via State-Space Transformation

“…This knowledge is reflected by the Biolek window [14], which depends not only on the state but also on the device current, or, more exactly, on its direction. Let us mention for the sake of completeness that also other window functions for modeling the nonlinear dopant drift can be found in the literature [15], [16], for example the Strukov [1], Prodromakis [17], TEAM or Kvatinsky [18] windows, the piecewise-linear window [19], the Tukey window [20], the trigonometric windows [21], the BCM [22] and generalized BCM model [23], etc. Some of the above techniques were developed in an effort to refine the models in order to make them conform to experimental data.…”