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arXiv · 1008.2528

Dynamical properties of electrical circuits with fully nonlinear memristors

Ricardo Riaza
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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 $v=η(q, i)$ 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 $η(q,i)$ 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 $i=ζ(φ, v)$. 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.

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Ricardo Riaza. 2010-08-15. Dynamical properties of electrical circuits with fully nonlinear memristors. https://arxiv.org/abs/1008.2528

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