Quantitative measure of hysteresis for memristors through explicit dynamics

Abstract

We introduce a mathematical framework for the analysis of the input-output dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli differential equation and hence can be nonlinearly transformed into a formally solvable linear equation. The Bernoulli formalism, which applies to both charge-and flux-controlled memristors when either current or voltage driven, can, in some cases, lead to expressions of the output of the device as an explicit function of the input. We apply our framework to obtain analytical solutions of the i-v characteristics of the recently proposed model of the Hewlett-Packard memristor under three different drives without the need for numerical simulations. Our explicit solutions allow us to identify a dimensionless lumped parameter that combines device-specific parameters with properties of the input drive. This parameter governs the memristive behaviour of the device and, consequently, the amount of hysteresis in the i-v. We proceed further by defining formally a quantitative measure for the hysteresis of the device, for which we obtain explicit formulas in terms of the aforementioned parameter, and we discuss the applicability of the analysis for the design and analysis of memristor devices.

Window functions and sigmoidal behaviour of memristive systems

“…An ideal memristor , as defined originally by Chua , is characterised by a unique and time‐invariant q − φ function with the following properties : and on the i − υ plane its canonical form is obtained from and . Under these conditions, the charge‐controlled and flux‐controlled functions are invertible, and these two representations of the memristor are equivalent .…”

The Memory-Conservation Theory of Memristance

“…As the theory stands in [3], w acts unphysically at the boundaries, this effect is corrected and nonlinearities are introduced at the device boundaries by the addition of window functions (see for example [9]- [11]). Most theoretical research has concentrated on using either Chua's theory [1], [12], Strukov's model [3] or an extension of it [13], although there has been some work in extending the model to a quantum domain [14]. In this paper, we will derive a novel description of the Strukov memristor by considering the electromagnetics of a uniform field across the whole device.…”

Current‐input current‐output analog half center oscillator and central pattern generator circuits with memristors

“…The analyses are conducted by Cadence Spectre simulations. The memristor model developed by Strukov et al which assumes linear ionic drift is used to model both the current‐driven and voltage‐driven memristors. We expect that the circuits will be robust to thermal noise based on calculations which show that noise current will be much smaller compared with excitation currents and based on previous studies on noise analysis with memristors demonstrating robustness to noise .…”