2.4 Genealogy of Memristor Devices
67
• current-controlled generic memristor
v = R(x)i
(2.40)
dx
dt
= f(x, i)
(2.41)
• voltage-controlled generic memristor
i = G(x)v
(2.42)
dx
dt
= g(x, v)
(2.43)
where x = (x 1 , x 2 , . . . , x n ) T is once more a vector of internal state variables.
Note the ideal generic memristor differs from a generic memristor only in
the form of the differential equation for the state variables; in the Eq. (2.26)
(resp., (2.28)) the r.h.s. is factorized so that f(·) (resp., g(·)) depends only on the
state vector x, whereas in the r.h.s. of (2.41) (resp., (2.43)) f(·) (resp., g(·)) depends
on both x and i (resp., v).
The PTC and NTC thermistors in Example 2.16, the discharge tube in Example 2.17, and the potassium and sodium ion channels of the Hodgkin–Huxley neuron
model in Example 2.18 belong to the class of generic memristors. The following
example presents a generic memristor as well.
Example 2.23 The ThrEshold Adaptive Memristor (TEAM) model proposed in
[34] is a passive Generic Memristor satisfying
v = R(x)i
where
dx(t)
dt
=
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
k off
i(t)
i off
− 1
α off
f off (x(t)), 0 < i off < i
0,
i off < i < i on
k on
i(t)
i on
− 1
α on
f on (x(t)), i < i on < 0.
In these equations, k off , k on , α off , α on are parameters (k off > 0, k on < 0) while i off
and i on (i on < 0 < i off ) represent current thresholds. Functions f off (x) > 0 and
f on (x) > 0, which are not necessarily equal, have the role of window functions and
they serve to constrain the state variable x in the interval [x on , x off ].
By turning off power, i.e., letting i = 0, we simply obtain
dx(t)
dt
= 0