Index
435
coupled inductors, 190
flux-controlled memristor, 187
independent current source, 186
independent voltage source, 185
inductor, 184
memcapacitor, 401
meminductor, 402
operational amplifier, 189
resistor, 185
time-varying capacitor, 191
time-varying memristor, 191
Extended memristor, 68, 375
asymmetric pinched hysteresis loop, 380
class D ext , 375
diode bridge, 71
ideal memristor and Shockley diode, 378
interconnection of basic circuit elements,
377
line of equilibrium points, 376
non-volatile, 376
nonlinear network synthesis, 381
power-off plot, 376
rectifying effects, 377
state-dependent Ohm’s law, 72
state variables, 377
volatile, 69
zero-crossing property, 375
Extended memristor and capacitor circuit, 382
convergence, 383
invariant manifolds, 383
Extreme multistability
array of Chua’s oscillators, 337
Chua’s oscillator with memristor, 261
mem-element circuits, 410
memristor capacitor circuit, 233
memristor memcapacitor circuit, 394
in M − L − C circuit, 249
F
Flux, 7
conservation of, 168
incremental, 177
Flux-charge analysis method (FCAM)
class LM, 179
class LME, 397
class LME , 420
class N D
N R , 287
extended memristor and capacitor circuit,
382
mem-element circuits, 389
memristor circuits, 179
multiport, 188
multiterminal, 188
reduced-order dynamics, 205
role of initial conditions, 198, 201
smoother dynamics, 205
time-varying elements, 191
Flux-charge domain
smoother dynamics in, 238
Flux momentum, 20, 389
Foliation of state space
Chua’s oscillator with memristor, 261
circuit with memristor and memcapacitor,
416
linear circuit, 222
M − L − C circuit, 246
Four basic circuit elements, 7
diagram of, 9
Four basic dynamic elements, 24
Fundamental cut-set, 104
Fundamental cut-set matrix, 104
Fundamental loop, 104
Fundamental loop matrix, 106
Fundamental topological assumption, 282
G
Gedanken experiment, 4
Generic memristor, 66
Graph
directed, 101
of a network, 101
theory, 101
H
Higher order circuit elements
algebraic, 17, 389
dynamic, 25
Hodgkin–Huxley model
potassium ions channels, 57
sodium ions channels, 57
HP memristor, 63, 84, 347
Joglekar window, 347
Hybrid representation of multiport
flux-charge domain, 281
voltage-current domain, 128
I
Ideal generic memristor, 61
siblings, 61
state variable transform, 63
Ideal memristor, 61
Impasse point, 134, 284
breaking of, 142
dynamic route, 134
435
coupled inductors, 190
flux-controlled memristor, 187
independent current source, 186
independent voltage source, 185
inductor, 184
memcapacitor, 401
meminductor, 402
operational amplifier, 189
resistor, 185
time-varying capacitor, 191
time-varying memristor, 191
Extended memristor, 68, 375
asymmetric pinched hysteresis loop, 380
class D ext , 375
diode bridge, 71
ideal memristor and Shockley diode, 378
interconnection of basic circuit elements,
377
line of equilibrium points, 376
non-volatile, 376
nonlinear network synthesis, 381
power-off plot, 376
rectifying effects, 377
state-dependent Ohm’s law, 72
state variables, 377
volatile, 69
zero-crossing property, 375
Extended memristor and capacitor circuit, 382
convergence, 383
invariant manifolds, 383
Extreme multistability
array of Chua’s oscillators, 337
Chua’s oscillator with memristor, 261
mem-element circuits, 410
memristor capacitor circuit, 233
memristor memcapacitor circuit, 394
in M − L − C circuit, 249
F
Flux, 7
conservation of, 168
incremental, 177
Flux-charge analysis method (FCAM)
class LM, 179
class LME, 397
class LME , 420
class N D
N R , 287
extended memristor and capacitor circuit,
382
mem-element circuits, 389
memristor circuits, 179
multiport, 188
multiterminal, 188
reduced-order dynamics, 205
role of initial conditions, 198, 201
smoother dynamics, 205
time-varying elements, 191
Flux-charge domain
smoother dynamics in, 238
Flux momentum, 20, 389
Foliation of state space
Chua’s oscillator with memristor, 261
circuit with memristor and memcapacitor,
416
linear circuit, 222
M − L − C circuit, 246
Four basic circuit elements, 7
diagram of, 9
Four basic dynamic elements, 24
Fundamental cut-set, 104
Fundamental cut-set matrix, 104
Fundamental loop, 104
Fundamental loop matrix, 106
Fundamental topological assumption, 282
G
Gedanken experiment, 4
Generic memristor, 66
Graph
directed, 101
of a network, 101
theory, 101
H
Higher order circuit elements
algebraic, 17, 389
dynamic, 25
Hodgkin–Huxley model
potassium ions channels, 57
sodium ions channels, 57
HP memristor, 63, 84, 347
Joglekar window, 347
Hybrid representation of multiport
flux-charge domain, 281
voltage-current domain, 128
I
Ideal generic memristor, 61
siblings, 61
state variable transform, 63
Ideal memristor, 61
Impasse point, 134, 284
breaking of, 142
dynamic route, 134