58
2 Fundamental Properties of Mem-Elements
C
g Na
E Na
g K
E K
G L
E L
i Na (t)
i K (t)
i L (t)
+
i(t)
Extracellular medium
−
Intracellular medium
v(t)
Fig. 2.21 Memristor-based Hodgkin–Huxley axon membrane circuit model derived in [1]. Circuit
parameters are: C = 1 µF/cm 2 , G L = 0.3 mS/cm 2 , E Na = 115 mV, E K = 12 mV, E L =
−10.613 mV, g K [n(t)] = ¯
g K n 4 (t), and g Na [m(t), h(t)] = ¯
g Na h(t) m 3 (t), where ¯
g K =
36 mS/cm 2 , ¯
g Na = 120 mS/cm 2 whereas n(t), m(t), and h(t) are governed by Eqs. (2.21), (2.23),
and (2.24), respectively
i Na = g Na [m, h]v Na =
¯
g Na h m
3
v Na
The memristor-based Hodgkin–Huxley axon circuit model, with the time-varying
potassium and sodium conductances respectively replaced by a first- and secondorder memristor, is shown in Fig. 2.21, where the values of all the circuit parameters
are also reported. The POP associated with the potassium ion-channel memristor
shows that it is volatile. The sodium ion-channel memristor cannot be studied by
means of the POP because it has two internal state variables (m, h).
2.4 Genealogy of Memristor Devices
For practical and didactic purposes, it is useful to introduce a hierarchical classification of memristive devices and systems [4, 24]. The following categorization
and nomenclature are commonly used to distinguish the different complexity in the
state-dependent Ohm’s law describing a memristive device:
• ideal memristor
• ideal generic memristor
• generic memristor
• extended memristor
Hereinafter, we refer to the nomenclature reported above.
2 Fundamental Properties of Mem-Elements
C
g Na
E Na
g K
E K
G L
E L
i Na (t)
i K (t)
i L (t)
+
i(t)
Extracellular medium
−
Intracellular medium
v(t)
Fig. 2.21 Memristor-based Hodgkin–Huxley axon membrane circuit model derived in [1]. Circuit
parameters are: C = 1 µF/cm 2 , G L = 0.3 mS/cm 2 , E Na = 115 mV, E K = 12 mV, E L =
−10.613 mV, g K [n(t)] = ¯
g K n 4 (t), and g Na [m(t), h(t)] = ¯
g Na h(t) m 3 (t), where ¯
g K =
36 mS/cm 2 , ¯
g Na = 120 mS/cm 2 whereas n(t), m(t), and h(t) are governed by Eqs. (2.21), (2.23),
and (2.24), respectively
i Na = g Na [m, h]v Na =
¯
g Na h m
3
v Na
The memristor-based Hodgkin–Huxley axon circuit model, with the time-varying
potassium and sodium conductances respectively replaced by a first- and secondorder memristor, is shown in Fig. 2.21, where the values of all the circuit parameters
are also reported. The POP associated with the potassium ion-channel memristor
shows that it is volatile. The sodium ion-channel memristor cannot be studied by
means of the POP because it has two internal state variables (m, h).
2.4 Genealogy of Memristor Devices
For practical and didactic purposes, it is useful to introduce a hierarchical classification of memristive devices and systems [4, 24]. The following categorization
and nomenclature are commonly used to distinguish the different complexity in the
state-dependent Ohm’s law describing a memristive device:
• ideal memristor
• ideal generic memristor
• generic memristor
• extended memristor
Hereinafter, we refer to the nomenclature reported above.