68
2 Fundamental Properties of Mem-Elements
which means that any x ∈ [x on , x off ] is a stable EP. The TEAM model is then a
nonvolatile generic memristor. This result is in accordance with Theorem 2.2.
2.4.4 Extended Memristor
A memristor is called an extended memristor if it’s defined by a state-dependent
Ohm’s law in which the memristance R(x, i) (resp. memductance G(x, v)) has the
following properties:
(a) it is a function of not only the state variables x, but also of the input current i
(resp., voltage v)
(b) it assumes only finite values when i = 0 (resp. v = 0), thus the memristance
R(x, 0) (resp., the memductance G(x, 0)) is a bounded and differentiable
function in a neighborhood of (x, 0) for any x ∈ R n .
Hence, an extended memristor is described by the following DAEs in the (v, i)domain:
• current-controlled extended memristor
v = R(x, i)i
(2.44)
dx
dt
= f(x, i)
(2.45)
where R(x, i) is bounded in a neighborhood of (x, 0) for any x
• voltage-controlled extended memristor
i = G(x, v)v
(2.46)
dx
dt
= g(x, v)
(2.47)
where G(x, v) is bounded and differentiable in a neighborhood of (x, 0) for any
x ∈ R n .
The Pt/TaO x /Ta-memristor in Example 2.15 is an extended memristor. A
further example is as follows.
Example 2.24 The NbO 2 –Mott memristor device in [35] is a passive voltagecontrolled extended memristor defined by the state-dependent Ohm’s law
i = G(x, v)v
=
σ 0 e
−
0.301
2k B T A
k B T
ω
2
1 +
ω
√
v/d
k B T
− 1
e
ω
√
v/d
k B T
+
1
2d
v