  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.
