2.3 Memristive Devices and Systems
55
When power is off, i.e., letting v = 0, we have
dx
dt
= g(x, 0) = 0
thus the POP is zero over the domain [0, 1] and so any ¯
x ∈ [0, 1] is a stable EP.
We conclude that the Pt/TaOx/Ta memristive device is a nonvolatile memory
memristor. Since the memristive device is passive, this result is in accordance with
Theorem 2.2.
Remark 2.4 In addition to the memristive device in Example 2.15, Theorem 2.2 is
confirmed experimentally by several physical passive devices. Experimental observations in a memristor device based on aluminum-oxide thin-film reveal a range of
nonvolatile resistive states that can be changed continuously by applying suitable
voltage pulses (Fig. 12 in Hickmott’s work [17]). Similar switching phenomena
are also displayed by memristive device and systems based on different materials
(nickel oxide, silicon monoxide, various molecular compounds as polyconjugated
compounds, phthalocyanines, and charge transfer complexes and SrZrO 3 ) [18–20].
Remark 2.5 It is worth remarking that Theorem 2.2 is valid also in the special case
of an ideal memristor (cf. Sect. 2.2.1).
For what concern volatile memristive devices, the chief examples are the
thermistor [1, 21], the discharge tube [22], and the potassium and sodium ion
channels of the Hodgkin–Huxley neuron model [23].
Example 2.16 (Thermistor) A Positive Temperature Coefficient (PTC) thermistor
is a memristive device defined by
i = G(T )v
and
˙
T =
δ P
H CP
(T 0P − T ) +
G(T )v 2
H CP
where
G(T ) =
R 0P exp {β P (T − T 0P )}
−1 .
The state variable T is given by the PTC thermistor body temperature and
δ P , H CP , T 0P , R 0P , β P are positive parameters.
By switching off power, i.e., letting v = 0, we obtain
˙
T =
δ P
H CP
(T 0P − T ).
55
When power is off, i.e., letting v = 0, we have
dx
dt
= g(x, 0) = 0
thus the POP is zero over the domain [0, 1] and so any ¯
x ∈ [0, 1] is a stable EP.
We conclude that the Pt/TaOx/Ta memristive device is a nonvolatile memory
memristor. Since the memristive device is passive, this result is in accordance with
Theorem 2.2.
Remark 2.4 In addition to the memristive device in Example 2.15, Theorem 2.2 is
confirmed experimentally by several physical passive devices. Experimental observations in a memristor device based on aluminum-oxide thin-film reveal a range of
nonvolatile resistive states that can be changed continuously by applying suitable
voltage pulses (Fig. 12 in Hickmott’s work [17]). Similar switching phenomena
are also displayed by memristive device and systems based on different materials
(nickel oxide, silicon monoxide, various molecular compounds as polyconjugated
compounds, phthalocyanines, and charge transfer complexes and SrZrO 3 ) [18–20].
Remark 2.5 It is worth remarking that Theorem 2.2 is valid also in the special case
of an ideal memristor (cf. Sect. 2.2.1).
For what concern volatile memristive devices, the chief examples are the
thermistor [1, 21], the discharge tube [22], and the potassium and sodium ion
channels of the Hodgkin–Huxley neuron model [23].
Example 2.16 (Thermistor) A Positive Temperature Coefficient (PTC) thermistor
is a memristive device defined by
i = G(T )v
and
˙
T =
δ P
H CP
(T 0P − T ) +
G(T )v 2
H CP
where
G(T ) =
R 0P exp {β P (T − T 0P )}
−1 .
The state variable T is given by the PTC thermistor body temperature and
δ P , H CP , T 0P , R 0P , β P are positive parameters.
By switching off power, i.e., letting v = 0, we obtain
˙
T =
δ P
H CP
(T 0P − T ).