2010/08/15 by Ricardo Riaza, Riaza, Ricardo
Engineering · Mathematics · Neuroscience · Physics and Astronomy · #05C50 #15A18 #34A09 #94C05 #Advanced Memory and Neural Computing #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Neural dynamics and brain function #cond-mat.mes-hall #math.DS #msc:05C50 #msc:15A18 #msc:34A09 #msc:94C05 #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1008.2528
19 pages
arxiv created 2010/08/15 · openalex publication_date 2010/08/15 · arxiv updated 2010/08/17 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
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.