Index
437
pinched hysteresis loop, 31, 41
symmetry, 42
PSpice implementation, 86
shifted characteristic, 192
tuning via impulses, 47
window functions, 66
zero-crossing property, 31, 41
zero phase-shift property, 31
Memristor capacitor circuit, 175
bifurcations without parameters, 233
coexisting monostable and multistable
dynamics, 235
conservation of charge, 227
dynamic route, 228, 239, 241
extreme multistability, 233
flux-charge domain, 206
foliation of state space, 233
impasse points, 239
invariant manifolds, 226, 273
multiple equilibrium points, 230
pulse programming, 273, 299
non-planar manifolds, 228
reduced-order dynamics, 228
saddle-node bifurcations without
parameters, 228
Memristor cellular neural networks (CNNs),
345
bounded solutions, 358
computing in memory, 369
computing in the flux-charge domain, 345
continuum of equilibrium points, 361
convergence for nonsymmetric
interconnections, 369
convergence for symmetric
interconnections, 358
gradient-type, 358
hole filling, 366
horizontal line detection, 362
for image processing, 361
Łojasiewicz inequality, 358
Lyapunov function, 359
multistability, 362
trajectories with finite length, 358
Memristor circuits
autonomous, 296
bad modeled, 243
class LM, 163
with impasse points, 243
with no external sources, 297
non-isolated equilibrium points, 224,
225
Memristor devices
genealogy of, 58
Memristor memcapacitor circuit, 391
bifurcations without parameters, 393
coexisting bistable and monostable
dynamics, 394
dynamic route, 394
extreme multistability, 394
invariant manifolds, 393
programming with pulses, 395
Memristors in antiparallel, 346
Memristor star cellular neural network, 307
M-L-C circuit, 243
coexisting oscillatory dynamics, 249
foliation of state space, 248
Hopf bifurcations without parameters, 247
invariant manifolds, 246
planar manifolds, 246
Multiple operating point paradox, 138
Multiple operating points, 138
Multiport elements, 188
Multiterminal elements, 188
N
NbO 2 -Mott memristor, 69
Negative impedance converter (NIC), 134
Negative resistance oscillator, 139
Node, 100
Nonlinear capacitor, 13, 398, 420
locally active, 13
locally passive, 13
Nonlinear dynamics
complex, 261
convergent
bistability, 233
estreme multistability, 233, 358
monostability, 233
multistability, 233, 358
oscillatory, 249
reduced-order, 298, 303, 306
Nonlinear inductor, 14, 398, 421
locally active, 14
locally passive, 14
Nonlinear resistor, 10
locally active, 11
locally passive, 11
piecewise linear characteristic, 132
strongly passive, 128
O
Ohm’s law, 5
state-dependent, 15
Operating point, 11
437
pinched hysteresis loop, 31, 41
symmetry, 42
PSpice implementation, 86
shifted characteristic, 192
tuning via impulses, 47
window functions, 66
zero-crossing property, 31, 41
zero phase-shift property, 31
Memristor capacitor circuit, 175
bifurcations without parameters, 233
coexisting monostable and multistable
dynamics, 235
conservation of charge, 227
dynamic route, 228, 239, 241
extreme multistability, 233
flux-charge domain, 206
foliation of state space, 233
impasse points, 239
invariant manifolds, 226, 273
multiple equilibrium points, 230
pulse programming, 273, 299
non-planar manifolds, 228
reduced-order dynamics, 228
saddle-node bifurcations without
parameters, 228
Memristor cellular neural networks (CNNs),
345
bounded solutions, 358
computing in memory, 369
computing in the flux-charge domain, 345
continuum of equilibrium points, 361
convergence for nonsymmetric
interconnections, 369
convergence for symmetric
interconnections, 358
gradient-type, 358
hole filling, 366
horizontal line detection, 362
for image processing, 361
Łojasiewicz inequality, 358
Lyapunov function, 359
multistability, 362
trajectories with finite length, 358
Memristor circuits
autonomous, 296
bad modeled, 243
class LM, 163
with impasse points, 243
with no external sources, 297
non-isolated equilibrium points, 224,
225
Memristor devices
genealogy of, 58
Memristor memcapacitor circuit, 391
bifurcations without parameters, 393
coexisting bistable and monostable
dynamics, 394
dynamic route, 394
extreme multistability, 394
invariant manifolds, 393
programming with pulses, 395
Memristors in antiparallel, 346
Memristor star cellular neural network, 307
M-L-C circuit, 243
coexisting oscillatory dynamics, 249
foliation of state space, 248
Hopf bifurcations without parameters, 247
invariant manifolds, 246
planar manifolds, 246
Multiple operating point paradox, 138
Multiple operating points, 138
Multiport elements, 188
Multiterminal elements, 188
N
NbO 2 -Mott memristor, 69
Negative impedance converter (NIC), 134
Negative resistance oscillator, 139
Node, 100
Nonlinear capacitor, 13, 398, 420
locally active, 13
locally passive, 13
Nonlinear dynamics
complex, 261
convergent
bistability, 233
estreme multistability, 233, 358
monostability, 233
multistability, 233, 358
oscillatory, 249
reduced-order, 298, 303, 306
Nonlinear inductor, 14, 398, 421
locally active, 14
locally passive, 14
Nonlinear resistor, 10
locally active, 11
locally passive, 11
piecewise linear characteristic, 132
strongly passive, 128
O
Ohm’s law, 5
state-dependent, 15
Operating point, 11