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| Авторизация |
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| Holden A.V. — Chaos |
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| Предметный указатель |
Action potential 239 257
Adaptability of biological systems 5 9
Adaptability, theory 4 7
Alternating periodicity and chaos 233
Area-preserving maps 79
Arnold diffusion 309
Arnold horn/tongue 58 66 69 70 71 74 167 241 242 243
Arnold’s cat map 84 86
Attractor 16
Attractor, Brouwer 90
Attractor, closed curve 16
Attractor, fixed point 16 197
Attractor, reconstruction of 17 168 286
Attractor, San Marco 78
Attractor, sink 16
Attractor, strange 12 15 19 26 58 59 72 85 88 90 91 95 112 122 124—127 158—159 197 198 212 278 286 291 293
Basin of attraction 28 239 261 293 294
Belousov — Zhabotinskii reaction 159 168 187 188 234
Bifurcation 41
Bifurcation, diagram 224
Bifurcation, flip 41 42 43 44 61
Bifurcation, fold 42 68
Bifurcation, heteroclinic 112
Bifurcation, Homoclinic 112 130
Bifurcation, Hopf 58 61 62 63 66 68 69 74 75 113 185 193 212 215 226 257 258
Bifurcation, map/diagram 46
Bifurcation, of circle maps 238 241
Bifurcation, of fixed points 16 41—42
Bifurcation, period douhling 21 44 188 193 229 253
Bifurcation, pitchfork 229
Bifurcation, point 7 275
Bifurcation, reverse 22
Bifurcation, saddle-node 257
Bifurcation, tangent 229 243 246
Bifurcation, transcritical 41 61 74
Binary representation 53 54
Binary shift register 277
Bistability 144 244
Bits (of information) 276 277
Boettcher function 49 79
Brownian motion 8 292
Brusselator 31 213 224 232 261
Calcium-cyclic AMP system 179 180 183 185
Cantor, function 241
Cantor, set 19 59 72 78 87 88 89 121 223 224 299
Cardiac, arrhythmia 197 238 253
Cardiac, dysrhythmia 234
Cardiac, fibrillation 252
Cardiac, rhythm 237
Cellular automaton 316
Central nervous system 6
Centre see “Fixed point”
Chemical kinetics 3 25
Coarse graining 291 309
Coherence 138
Compartments 6 7
Complex maps 77—79
Complex plane 43 58 77
Computer 46
Conservative system 281
Contraction mapping theorem 185
Control theory 99 180 187
Convection 112
Correlation, exponent 303
Correlation, integral 107
Correlation, spectrum 232
Crisis in adaptability theory 6
Delay-differential equations 160—161
Devil’s staircase 167
Dimension, correlation 201
Dimension, fractal 19 78 107 129 159 170 174 175 180 281 287 289 293
Dimension, Hausdorf 170 175 293
Dimension, information 292 296
Dissipative structure 257
DNA, parasitic 12
Doppler shift 139
Doppler shift of attractor 194 196
Douady’s rabbit 79
Duffing’s equation 28
Dynamical disease 196
Dynamo, disk 20
Ecosystem dynamics 11
Entrapment 11 188 215 226
Entropies of adaptability theory 5 6
Entropies, Hausdorf 201
Entropies, Kolmogorov — Sinai (or metric) 231 292 294 296 309
Entropies, Renyi 295 304
Enzyme, activation 182
Enzyme, allosteric 188
Epileptic seizure 180
Ergodic systems 56 86 230
Evolution 4 5 6 11
Excitable, (membrane) 10
Excitable, media 238 252
Faraday effect 141
Farey series 167 245 260
Feedback system 99 101 104 105 108 182 183 192
Feigenbaum constant 44 51 72 150 226 229
Fixed point 59
Fixed point, attractor see “Attractor”
Fixed point, centre 60
Fixed point, elliptic 82
Fixed point, focus 60
Fixed point, hyperbolic 82 88
Fixed point, multiplier 47 59
Fixed point, node 59 211 212
Fixed point, of map 40
Fixed point, saddle 60 61 114
Fixed point, star node 61
Focus see “Fixed point”
Folding see “Stretching and folding”
Forced oscillator’s 28—33 165 211—235
Fourier, spectrum 188 289
Fourier, transform 211 232
Fractal, basin boundary 167
Fractal, dimension see “Dimension”
Gaussian distribution 172 175
Genetic variability 8 9
Glycolysis 33 180 181 183 188 234
Golden ratio 84
Goodwin equations 184
Gram — Schmidt reorthonormalisation (GSR) 283—286
H-Theorem 13
Hamiltonian 79 136 309 316
Harmonic balance 107
Heisenberg equation of motion 137
Henon attractor 282 284 285 287 288 299 303 308
Heteroclinic orbits 114
Hierarchy 6
Hodgkin — Huxley equations 194 257—266
Homeostasis 179
Homoclinic orbits 113—124 127 131
Homoclinic point 58 83 88
Homoclinic tangency 223
Hopf bifurcation see “Bifurcation”
Hopf bifurcation, circle 67 68 70 72
Hopf bifurcation, radius 67 68 71
Host-parasitoid model 58 75
Hyperchaos 26 319
Immune system 4 6 8 9 10
| Infectious diseases 165
information 292
Information, flow 305
Intermittency 111 129 153 188 243 246 264 266
Invariant, curve 61
Invariant, distribution 52 54 85
Invariant, measure 56 85 230 231
Island 83 226 261
Isochron 239
Josephson junction 107
Julia set 58 78 79
KAM, curve 84
KAM, theorem 81 84
Khinchin axioms 300 303
Kneading 222 226
Kolmogorov, entropy 194
Kolmogorov, exponent 194
Laser, homogeneously broadened single mode 135 141—144
Laser, inhomogeneously broadened 135 136 152—155
Legesgue measure 53
Light-atom interactions, semiclassical approximation 135 136—140
Limit cycle 16 32 212 239
Lipschitz norm 104
Logistic map 43—45 54 159 162 274
Logistic-delay equation, (two dimensional) 62 65
Logistic-delay equation, differential-delay 160
Loop delay 186
Lorenz system 19 21 111—132 141 142 143 152 160 161 234 278 279 281 287 288 303 308 309
Lotka — Volterra equations 161
Low frequency noise 144
Lyapunov, exponent 18 26 52 56 86 87 107 167 194 195 201 273—289 295 297 304 308
Lyapunov, number 230 231 266
Lyapunov, spectrum 277—289
Manifold, fast 221 228
Manifold, intersection of 58
Manifold, invariant 59
Manifold, slow 220 221 228
Manifold, stable 58 61 62
Manifold, unstable 58 59 61 62 71 83 88 89 230
Map, non-invertible 148 161 219
Map, one-dimensional 126 128 143 159 161 172 188 219 228 242 274 285
Map, return 118 124 125 128 162 188
Map, two parameter circle 240 243 252
Maser 141
Maxwell equation 138 141
Maxwell — Bloch equations 112 138 139 140 145 146
Membrane excitability 10
Mobius band 21
Modifiabiltties 6 7
Monte Carlo methods 55 85
Multiplier 40 41 47 63 81
Natural selection 4
Neurone dynamics 3 4 180 190 257—267
Node see “Fixed point”
Noise 171
Noisy periodicity 129
Normal form 63 66 67 70
Nyquist, locus 184 t85 186
Nyquist, stability theorem 184
Optical bistability 135 141 145 146
Optical chaos 135
Optical resonator 139
Optimization 108
Oscillator, glycolytic 33
Oscillator, negative resistance 30
Parametrisiation of orbit 46—48
Period doubling 21 26 44 49—52 145 146 148 150 153 161 167 171 226 243 247—249 264
Period doubling, universality 50
Period-3 solution 188
Periodic orbit 122 123 128 131 275
Periodic point 40
Perron — Frobenious equation 53 55 85
Phase 239
Phase, diagram 224
Phase, locking 240 241 244 245
Phase, transition curve 239 240 241 242 243 244 249
Poincaire, equation 47 62
Poincaire, function 47 49
Poincaire, map 81 239 240 244
Poincaire, section 162 170 215 218 289
Polarisation 138
Population dynamics 3 10 39 58 71 234
Prandtl number 19
Predator-prey mode! 58 74 100 158 159 161 167
probability density 275
Pulse-Width Modulation 102 104
Quadratic mappings see also “Logistic map”
Quadratic mappings, one dimensional 39
Quadratic mappings, two dimensional 39 58
Quantum operator 137
Quantum turbulence 155
Quasi-periodicity 158 165 167 215 216 226 240 243 249 260 264 266
Rabi frequency 137 139 141
Random 3 4
Rayleigh number 19
Relaxation oscillation 220
Renormalisation 51 226
Renyi informations 300 302 303
Repeller, snap-back 102
Resonance 64 66 70 71 166 167 213 214
Resonator (optical), Fabry — Perot 141
Resonator (optical), passive 135
Resonator (optical), unidirectional ring cavity 139 140
Reynold’s number 288
Rossier, 3-D system 21—24 105 160 161 165
Rossier, hyperchaos 26 288
Rotation number 82 84 240 241 242 245 260
Round-off 46
Routes to chaos 243 244
Ruelle — Takens route 150 153
Saddle see “Fixed point”
Seizure 199 201
Self-similar 83 87 90
Sensitivity to initial conditions 18 122 159 212 218 237 273 291
Shannon information 302
Smale’s axiom A 112
Smale’s horseshoe 88 123 159 212 213 219 223 224
Spectral analysis 107
Standard map 81
Strange Attractor see “Attractor”
Strange invariant set 122 124
Stretching 275
Stretching and folding 3 18 119 125 168 171 223 277 316
Stroboscopic portrait 30 219 220 258
Stroboscopic transfer function 188 288—189
Structural stability 7 13 218
Superstate cycle 240 241 243 276
Symbolic dynamics 121 123
Taylor — Couette flow 168 288 293
Tent map 53
Transition scheme 5 7 8
Tremor 197 199
Twist map 81
Two-level atom 137
Two-symbol shift 88
Uncertainty 5 7
Universality 50 150 155 229 242 243
van der Pol oscillator 107 212 213 216 238 239
Variability, genetic 8 9
Window 45 164 229 233 276
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