434
Index
Chua’s oscillator with memristor (cont.)
foliation of state-space, 261
invariant manifolds, 256
non-planar invariant manifolds, 258
period-doubling bifurcations without
parameters, 257
reduction of order, 261
spiral chaotic attractor, 259
Circuit changing topology, 176
Circuit element(s), 3
(α, β), 18
algebraic, 23
characteristic, 10
distributed, 6
dynamic, 23
lumped, 6
periodic table, 23
Circuit with memristor and memcapacitor, 411
bifurcation diagram, 414
coexisting attractors, 416
coexisting dynamics, 416
extreme multistability, 416
pulse programming, 416
Circuit with tunnel diode, 138, 144
Coexisting dynamics
array of Chua’s oscillators, 334
Chua’s oscillator with memristor, 261, 303
mem-element circuits, 410
memristor capacitor circuit, 235
memristor memcapacitor circuit, 393
M − L − C-circuit, 247
Complex attractor, 149
Computing in memory, 345
Conductance, 10
Conservation of
charge, 168
flux, 168
incremental charge, 170
incremental flux, 170
Constitutive relation, 5
flux-charge domain, 182
capacitor, 182
charge-controlled memristor, 187
controlled source, 189
coupled inductors, 190
flux-controlled memristor, 186
independent current source, 185
independent voltage source, 185
inductor, 183
memcapacitor, 401
meminductor, 402
operational amplifier, 189
relevant two-terminal elements, 276
resistor, 184
time-varying capacitor, 191
time-varying memristor, 191
memcapacitor, 19
meminductor, 20
memristor, 15
nonlinear capacitor, 13
nonlinear inductor, 14
nonlinear resistor, 10
voltage-current domain
memcapacitor, 402
meminductor, 403
Convention
active, 101
passive, 101
Cotree, 102
Current, 4
higher order derivatives and integrals (i (β) ),
6
Current momentum (charge), 7
Cut-set, 102
D
Device model, 4
axiomatic approach, 4
black-box approach, 4
Differential algebraic equations, 134
flux-charge domain, 197
tableau analysis, 198
voltage-current domain, 109, 201
Digraph, 101
Discharge tube, 56
Dynamic route, 132
impasse points, 134
E
Element closure property, 23
Element independence property, 23
Equations
cut-set, 104
loop, 100
node, 100
Equilibrium point, 132
asymptotically stable, 133
attraction basin, 233
multiple, 230
non-isolated, 224, 225
single, 230
unstable, 133
Equivalent circuit
flux-charge domain
capacitor, 183
charge-controlled memristor, 187
controlled source, 189
Index
Chua’s oscillator with memristor (cont.)
foliation of state-space, 261
invariant manifolds, 256
non-planar invariant manifolds, 258
period-doubling bifurcations without
parameters, 257
reduction of order, 261
spiral chaotic attractor, 259
Circuit changing topology, 176
Circuit element(s), 3
(α, β), 18
algebraic, 23
characteristic, 10
distributed, 6
dynamic, 23
lumped, 6
periodic table, 23
Circuit with memristor and memcapacitor, 411
bifurcation diagram, 414
coexisting attractors, 416
coexisting dynamics, 416
extreme multistability, 416
pulse programming, 416
Circuit with tunnel diode, 138, 144
Coexisting dynamics
array of Chua’s oscillators, 334
Chua’s oscillator with memristor, 261, 303
mem-element circuits, 410
memristor capacitor circuit, 235
memristor memcapacitor circuit, 393
M − L − C-circuit, 247
Complex attractor, 149
Computing in memory, 345
Conductance, 10
Conservation of
charge, 168
flux, 168
incremental charge, 170
incremental flux, 170
Constitutive relation, 5
flux-charge domain, 182
capacitor, 182
charge-controlled memristor, 187
controlled source, 189
coupled inductors, 190
flux-controlled memristor, 186
independent current source, 185
independent voltage source, 185
inductor, 183
memcapacitor, 401
meminductor, 402
operational amplifier, 189
relevant two-terminal elements, 276
resistor, 184
time-varying capacitor, 191
time-varying memristor, 191
memcapacitor, 19
meminductor, 20
memristor, 15
nonlinear capacitor, 13
nonlinear inductor, 14
nonlinear resistor, 10
voltage-current domain
memcapacitor, 402
meminductor, 403
Convention
active, 101
passive, 101
Cotree, 102
Current, 4
higher order derivatives and integrals (i (β) ),
6
Current momentum (charge), 7
Cut-set, 102
D
Device model, 4
axiomatic approach, 4
black-box approach, 4
Differential algebraic equations, 134
flux-charge domain, 197
tableau analysis, 198
voltage-current domain, 109, 201
Digraph, 101
Discharge tube, 56
Dynamic route, 132
impasse points, 134
E
Element closure property, 23
Element independence property, 23
Equations
cut-set, 104
loop, 100
node, 100
Equilibrium point, 132
asymptotically stable, 133
attraction basin, 233
multiple, 230
non-isolated, 224, 225
single, 230
unstable, 133
Equivalent circuit
flux-charge domain
capacitor, 183
charge-controlled memristor, 187
controlled source, 189