Oscillatory Circuits With a Real Non-Volatile Stanford Memristor Model

Abstract

Stanford memristor model is a widely used model that accurately characterizes real non-volatile metal-oxide resistive random access memory (RRAM) devices with bipolar switching characteristics. The paper studies for the first time the dynamics and bifurcations in a class of nonlinear oscillators with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real non-volatile memristor devices</i> obeying Stanford model. This is in contrast with papers in the literature considering oscillators with ideal, abstract, or artificial memristor models, that are unable to describe physical memristors implemented in nanotechnology. One main new idea in the paper is to use the memristor as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">programmable nonlinear resistor</i> . Namely, two principal modes of operation are considered. 1) Analogue transient phase: the oscillator is designed so that in the transient oscillations the voltage on the memristor is below threshold, hence the main memristor state variable, i.e., the gap of the insulating material, is almost constant and the memristor behaves as a static nonlinear resistor. 2) Programming phase: the nonlinear characteristic of the memristor, which depends on the gap, can be changed via the application of voltages above threshold. The paper studies nonlinear oscillations in the transient phase for a fixed gap as well as the bifurcations phenomena displayed when the gap is varied. The paper also discusses the differences between the approach in the paper and those to design other memristor oscillators with non-volatile memristors.