436
Index
Incidence matrix, 105
reduced, 106
Incremental charge
conservation of, 181
Incremental flux
conservation of, 181
Inductance, 14
small-signal, 14
Initial state, 113
Initial value problem (IVP), 113
Invariant manifolds
circuits with mem-elements, 409
dynamic properties, 293
geometric properties, 293
linear circuit, 222
memristor capacitor circuit, 226
memristor memcapacitor circuit, 393
M − L − C circuit, 246
non-planar, 258
planar, 313
Invariant of motion, 297
Chua’s oscillator with memristor, 256
linear circuit, 222
memristor capacitor circuit, 226
M − L − C circuit, 246
J
Josephson junction, 14
Jump phenomenon, 142
Jump rule, 146
K
Kirchhoff Charge Law (KqL), 181
Kirchhoff Current Law (KCL), 100,
182
Kirchhoff flux law (KϕL), 181
Kirchhoff laws
flux-charge, 182
flux-charge domain, 167
voltage-current domain, 100
Kirchhoff Voltage Law (KVL), 100,
182
L
Limit cycle, 141
Link, 102
Loop, 100
Lyapunov approach, 358
Lyapunov method, 359
M
Memcapacitor, 19, 390
pinched hysteresis loop, 77
zero–crossing property, 77
Memductance, 15, 17
Mem-element circuits
bifurcations without parameters, 410
class N e , 390
classes LME and LME , 397
coexisting dynamics, 410
extreme mulstistability, 410
flux-charge domain
state equations, 408
invariant manifolds, 409
with nonlinear capacitors and inductors,
421
voltage-current domain
state equations, 408
Mem-elements
flux-charge domain
order reduction, 403
Meminductor, 20, 390
pinched hysteresis loop, 77
Memory capacitance, 20
Memory inductance, 21
Memristance, 15
Memristive devices and systems, 48
continuum of equilibrium states, 54
non–volatile memory, 51
Power–Off–Plot (POP), 51
two is infinity theorem, 54
volatile memory, 51
Memristor, 15
as an analog memory, 44
and capacitor element, 195
charge-controlled, 28, 187
continuum of equilibrium states, 44
cubic, 227
as a digital memory, 47
extended, 68
flux-controlled, 28, 186
generic, 66
ideal, 61
ideal generic, 61, 208
monotone non-decreasing characteristic, 29
neuromorphic applications, 343
no energy storage property, 30
non–volatile memory memristor, 44
parallel connection, 195
passivity property, 29
piecewise linear, 236, 382
Index
Incidence matrix, 105
reduced, 106
Incremental charge
conservation of, 181
Incremental flux
conservation of, 181
Inductance, 14
small-signal, 14
Initial state, 113
Initial value problem (IVP), 113
Invariant manifolds
circuits with mem-elements, 409
dynamic properties, 293
geometric properties, 293
linear circuit, 222
memristor capacitor circuit, 226
memristor memcapacitor circuit, 393
M − L − C circuit, 246
non-planar, 258
planar, 313
Invariant of motion, 297
Chua’s oscillator with memristor, 256
linear circuit, 222
memristor capacitor circuit, 226
M − L − C circuit, 246
J
Josephson junction, 14
Jump phenomenon, 142
Jump rule, 146
K
Kirchhoff Charge Law (KqL), 181
Kirchhoff Current Law (KCL), 100,
182
Kirchhoff flux law (KϕL), 181
Kirchhoff laws
flux-charge, 182
flux-charge domain, 167
voltage-current domain, 100
Kirchhoff Voltage Law (KVL), 100,
182
L
Limit cycle, 141
Link, 102
Loop, 100
Lyapunov approach, 358
Lyapunov method, 359
M
Memcapacitor, 19, 390
pinched hysteresis loop, 77
zero–crossing property, 77
Memductance, 15, 17
Mem-element circuits
bifurcations without parameters, 410
class N e , 390
classes LME and LME , 397
coexisting dynamics, 410
extreme mulstistability, 410
flux-charge domain
state equations, 408
invariant manifolds, 409
with nonlinear capacitors and inductors,
421
voltage-current domain
state equations, 408
Mem-elements
flux-charge domain
order reduction, 403
Meminductor, 20, 390
pinched hysteresis loop, 77
Memory capacitance, 20
Memory inductance, 21
Memristance, 15
Memristive devices and systems, 48
continuum of equilibrium states, 54
non–volatile memory, 51
Power–Off–Plot (POP), 51
two is infinity theorem, 54
volatile memory, 51
Memristor, 15
as an analog memory, 44
and capacitor element, 195
charge-controlled, 28, 187
continuum of equilibrium states, 44
cubic, 227
as a digital memory, 47
extended, 68
flux-controlled, 28, 186
generic, 66
ideal, 61
ideal generic, 61, 208
monotone non-decreasing characteristic, 29
neuromorphic applications, 343
no energy storage property, 30
non–volatile memory memristor, 44
parallel connection, 195
passivity property, 29
piecewise linear, 236, 382