# Dynamical properties of electrical circuits with fully nonlinear memristors

Riaza, Ricardo (2011). Dynamical properties of electrical circuits with fully nonlinear memristors. "Nonlinear Analysis: Real World Applications", v. 12 ; pp. 3674-3686.

## Description

Title: Dynamical properties of electrical circuits with fully nonlinear memristors Riaza, Ricardo Article Nonlinear Analysis: Real World Applications 2011 12 E.T.S.I. Telecomunicación (UPM) Matemática Aplicada a las Tecnologías de la Información [hasta 2014] None

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## Abstract

The recent design of a nanoscale device with a memristive characteristic has had a great impact in nonlinear circuit theory. Such a device, whose existence was predicted by Leon Chua in 1971, is governed by a charge-dependent voltage-current relation of the form $v=M(q)i$. In this paper we show that allowing for a fully nonlinear characteristic $v=\eta(q, i)$ in memristive devices provides a general framework for modeling and analyzing a very broad family of electrical and electronic circuits; Chua's memristors are particular instances in which $\eta(q,i)$ is linear in $i$. We examine several dynamical features of circuits with fully nonlinear memristors, accommodating not only charge-controlled but also flux-controlled ones, with a characteristic of the form $i=\zeta(\varphi, v)$. Our results apply in particular to Chua's memristive circuits; certain properties of these can be seen as a consequence of the special form of the elastance and reluctance matrices displayed by Chua's memristors.

Item ID: 10284 https://oa.upm.es/10284/ oai:oa.upm.es:10284 Dr Ricardo Riaza 13 Feb 2012 07:26 20 Apr 2016 18:30

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