August 15, 2010
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.
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We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux $\phi$ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based...
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The prediction made by L. O. Chua 45+ years ago (see: IEEE Trans. Circuit Theory (1971) 18:507-519 and also: Proc. IEEE (2012) 100:1920-1927) about the existence of a passive circuit element (called memristor) that links the charge and flux variables has been confirmed by the HP lab group in its report (see: Nature (2008) 453:80-83) on a successful construction of such an element. This sparked an enormous interest in mem-elements, analysis of their unusual dynamical propertie...
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