Memristor for Neuromorphic Applications: Models and Circuit Implementations

Abstract

The current-controlled ideal memristor is a passive bipole linking charge q(t) and flux ϕ(t) through a nonlinear relation, i.e. ϕ(t) = ϕ(q(t)). From application of Faraday's Law and of the chain rule it follows that voltage v(t) depends upon currentwheredq is the memristance (i.e. memory-resistance) of the bipole. SinceIn other words the resistance of the memristor depends upon the time history of the current flowed through it. This explains the memory capability of the memristor, theoretically envisioned by Chua in 1971 [1] and later classified by Chua and Kang in 1976 as the simplest element from a large class of nonlinear dynamical systems endowed with memristance, the so-called memristive systems [2].In [2] a memristive system (or memristor system 1 ) is a nonlinear dynamical circuit element defined by the following differential-algebraic system of equations: 1 In the following memristive systems are referred to as memristor systems, whereas the term ideal memristor is used for systems described by (13.1).A. Ascoli ( ) • R. Tetzlaff

Stochasticity Modeling in Memristors

“…The function θ is the step function responsible for enforcing this constraint. Incorporating the variability into this model follows a straightforward approach where the threshold voltage V t is varied in a way abiding by the stochasticity measures explained earlier and depicted in (13). It allows for sub-threshold switching in a non-deterministic fashion where the value of the point of switching is related to the input voltage application time and amplitude.…”

“…The memristor is central to this operation as well, and it has been considered in many applications to hold a close resemblance to the basic building blocks of the human brain architectures. In applications with biologically inspired stochastic computation [7], [8] and neuromorphic systems [9]- [13], as synapses [14], and neurons [15]- [18].…”

Spintronic memristor synapse and its RWC learning algorithm

“…In addition, the spintronic memristor is made of magnetic material and has a simple production process [3][4][5]. The spintronic memristive device with these advantages has been proved to be effective in a neural morphology system as a digital synapse [6][7][8][9][10][11].…”