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| Авторизация |
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| Gonzalez-Miranda J.M. — Synchronization and Control of Chaos: An Introduction for Scientists and Engineers |
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| Предметный указатель |
Amplification of a chaotic attractor 90 95
Amplitude envelope synchronization 156 160 172 187
Analytic signal 57 58 61 174
Anticipated synchronization 91 92 95 98 168
Antiphase synchronization 105 110
Aperiodic oscillation 16 18
Arnold tongue 68–70
Atmospheric circulation, coupled to oceanic circulation 194
Atmospheric circulation, Lorenz model 193
Atmospheric circulation, pattern of 193
Auxiliary system approach 100 101 104 109
Belusov — Zhabotinsky reaction 122
Bifurcation diagram 32 140
Bifurcation theory 31 32 183
Brain, large scale integration 189
Brain, specialized areas 190
Cardiac arrhythmias 122
Chaos suppression 70 71 73 76 77
Chaos suppression by a external force 71 75 184
Chaos suppression by parametric perturbation 71 72 76
Chaos suppression, phase effects 74 76
Chaotic attractor 18 20 27 52 182
Chaotic communications 194
Chaotic communications, control of chaos 196
Chaotic communications, masking and recovery 195
Chemical chaos 50 120
Chemical oscillator 69 77 95 129 153 174
Chua circuit 26 88
Chua circuit, Double Scroll attractor 32
Chua circuit, identical synchronization 97
Chua circuit, marginal synchronization 91 95 97
Chua circuit, motion in a torus 27
Chua circuit, mutually coupled 144 172 176
Chua circuit, period doubling route to chaos 29
Chua circuit, return map 29 32
Clustering 147 179
Coherent chaotic oscillators 70 173
Collective behavior 134
Complete synchronization 186
Continuous control 123
Control law 113 114 117 119 124
Control matrix 114 117
Control of chaos 114 119 196
Control of chaos, delayed feedback control 124 125 128
Control of chaos, effect of noise 119 127
Control of chaos, OGY method 116 120
Control of chaos, perturbation stiffness 131
Control of chaos, transitory 119
Control parameter 113 115
Controlling force 125
Correlation coefficient 157 158
Coupling matrix 148 176
Crisis 31 139 143
Delayed equations 21 91
Delayed feedback control 123 125 128 131 185
Delayed variable 21 92
Difference equation 22
Diffusive coupling 134 148 155
Discharge plasma 68 77
Displacement of a chaotic attractor 90 97
Dissipation 5 7 12 19
Driven pendulum 13
Duffing oscillator 13 71
Duffing oscillator, aperiodic oscillations 15
Duffing oscillator, chaos control 125
Duffing oscillator, chaos suppression 75
Duffing oscillator, synchronization 95
Ecology 180
Electric circuit 96 108
Electric circuit, chaotically driven 97 109
Electric circuit, periodically driven 70
Electric circuit, RLC circuit 9
Electric circuits, mutually coupled 144 152 175
Electrochemical cell 129 153 174
Electrochemical corrosion 129
Electroencephalography 191 192
Embedding techniques 52 58 68 77
Embedding techniques, embedding dimension 49
Embedding techniques, embedding space 49
Envelope of a dynamical variable 156
Equilibrium 18 32
Fixed point 18 112 114
Fixed point, stable 18
Fixed point, unstable 18 113
Flow 17 18 183
Fluid convection 19 123
Fractal 22 182
Frequency of a chaotic oscillator 41 54 55 59 60 159 160 163 176
Frequency of a periodic force 53
Frequency of a periodic oscillator 41
Frequency of an harmonic oscillator 5
Frequency, resonant 71 73 76 183
Generalized synchronization 108 191
Generalized synchronization, chaotically driven oscillators 100 102 106 184
Generalized synchronization, mutually coupled oscillators 168 187
Generalized time lagged, synchronization 168 176
Global coupling 148
harmonic oscillator 2 4 181
Henon map 22 116
Henon map, control of chaos 116
Henon map, fractal structure 22
Henon map, unstable periodic orbit 116
Hindmarsh — Rose model 41
Hindmarsh — Rose model, bursts and spikes 42
Hindmarsh — Rose model, power spectrum 43
Hyperchaotic attractor 36 140
Hyperchaotic oscillator, Rossler 173
Identical synchronization 83 86 100 191 195
Identical synchronization, chaotically driven oscillators 83 94 184
Identical synchronization, mutually coupled oscillators 135 139 186
Ikeda equation 21
Ikeda map 47
Ikeda map, unstable periodic orbits 48
interaction matrix 134 137 140
Josephson junction 73 75
Lag synchronization 167—169 172 187
Laser 76 97 109 146
Limit cycle 12
Linearity 6 182
Linearized equations 36 101 137
Logistic equation 22
Lorenz model 19 61
Lorenz model, anticipated synchronization 95
Lorenz model, generalized synchronization 102
Lorenz model, identical synchronization 81 84 94 97
Lorenz model, imperfect phase synchronization 70
Lorenz model, marginal synchronization 82 88 95
Lorenz model, mutually coupled 137 173
Lorenz model, predictability 19 21
Lyapunov exponent 33 73 75 82 91 108 140
Lyapunov exponent, calculation of 36
| Lyapunov exponent, conditional Lyapunov exponent 83 84 86 90 91 94 100 103
Lyapunov exponent, lag synchronization 170
Lyapunov exponent, longitudinal 138
Lyapunov exponent, meaning of 33
Lyapunov exponent, mutually coupled oscillators 138 159 166
Lyapunov exponent, transverse 137 138 141 149
Lyapunov function 84 101
Lyapunov spectrum 34 35 182
Mackey and Glass model 21
Mackey and Glass model, anticipated synchronization 92 94
Mackey and Glass model, mutually coupled 173
Macro-oscillation 134 149
Magneto-elastic system 120
Magneto-mechanical system 120 128
MAP 17 21 29 45 183
Marginal synchronization 87 95 108
Melnikov method 76
Motion in a torus 27 30
Multistability 139 143 150 153
Mutual coupling 134
Mutual false nearest neighbor parameter 101 103 108
Near synchronization 94
Nervous system 189
neuron 76 189
Neuron, bursting dynamics 42 190
Neuron, Hindmarsh — Rose model 41 189
Neuron, spiking dynamics 42 190
Neuronal populations 122
Nonlinear optics 21 47
Nonlinear optics, rign cavity 47
Nonlinearity 12 13
Normal modes 11 12 182
OGY method 112 185
Optical cavity 174
Parallel perturbation 136
Parametric plot 86 88 90 92 101
Partial phase synchronization of N coupled oscillators 177
Partial synchronization 150 152 186
Pattern formation 147 150
Period doubling 29
Period doubling, cascade 38 139
Periodic boundary conditions 149 150 177
Periodic force 7 53 62 67 70 71 76
Phase of a chaotic oscillator 54 55 57 58 62 173 183
Phase of a periodic force 53
Phase of an harmonic oscillator 5
Phase slip 63 66 163
Phase synchronization 191 193
Phase synchronization of mutually coupled oscillators 162 163 172 187
Phase synchronization of N coupled oscillators 176 177 180
Phase synchronization to a external force 54 62 64 66 68 70 183
Phase synchronization, imperfect 70
Physiological control 21
Poincare map 24 29 60 63 70 112
Poincare surface 24 112
Population dynamics 22 180
Population of oscillators 176—178
Power spectrum 40 41 67 160 182
Predictability 21 33 193
Projective synchronization 90
Proper rotation 54 55 57 58 63 67
Proper rotation, intrinsic modes 61 69
Proportional perturbation feedback 122 123
Proto-Lorenz model 172
Pyragas method 124 185
Quasiperiodic attractor 36 140
Reconstructed space 49
Resonance 8 9 182
Return map 26 29 32 60 63 70
Return time 25 26 60 70 159
Rossler model 37
Rossler model, anticipated synchronization 95
Rossler model, funnel attractor 39 173
Rossler model, generalized synchronization 102 108
Rossler model, identical synchronization 94
Rossler model, lag synchronization 169
Rossler model, Lyapunov spectrum 37
Rossler model, modified 163
Rossler model, mutually coupled 140
Rossler model, partial synchronization 150 151
Rossler model, phase synchronization 62 63 65 67 162
Routes to chaos, period doubling 29
Routes to chaos, quasi-periodicity 30
Sensitivity to initial conditions 33 182
Silnikov homoclinic chaos 50 52
Similarity function 92 168 169 175
Similarity function, generalized 168
Spatially extended systems 134 180
Spectral analysis 40
Spectral analysis of amplitude envelope synchronization 160
Spectral analysis of chaos suppression 73
Spectral analysis of phase synchronization 66 166
Spectral analysis, Fast Fourier Transform 40
Sprott attractors 95
Stability, asymptotic 83 90 93 95
Stability, marginal 90 95
Stability, orbital 91
Stability, structural 94 145
Stable equilibrium 4 6 12
Stable manifold 113 117
Strange Attractor 22
Stroboscopic plot 58 59 64 67 69
Suppression of chaos, mutually coupled oscillators 146
Surface of section 24 27 112
Symmetric chaotic systems 87 105
Synchronization manifold 135 136 149 152
Synchronization manifold, stability 135
Synchronized state 134 139 149 153
Synchronized state, stable 135
Synchronized state, unstable 135
Takens theorem 49
Taylor — Couette flow 129
Telecommunications 194
Thermo-optical system 174
Time delay 21 92
Transverse perturbation 136
Transverse subspace 135 136 149
Turbulence 123
Unidirectional coupling 79 88 94
Unidirectional coupling, continuous control 80 83 95
Unidirectional coupling, drive 80 88 99
Unidirectional coupling, replacement of variables 80 83 94
Unidirectional coupling, response 80 82 88 92 99
Unidirectional coupling, subsystem decomposition 82 84 87 94
Unstable manifold 113 117
Unstable periodic orbit 44 48 112 124 131 182
Van der Pol-Duffing oscillator, amplitude envelope synchronization 157 160
Van der Pol-Duffing oscillator, phase of a chaotic oscillator 55 58 59
Vector field 18
Vector field, Jacobian matrix of 36
Weather predictability 19
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