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Gonzalez-Miranda J.M. — Synchronization and Control of Chaos: An Introduction for Scientists and Engineers
Gonzalez-Miranda J.M. — Synchronization and Control of Chaos: An Introduction for Scientists and Engineers

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Название: Synchronization and Control of Chaos: An Introduction for Scientists and Engineers

Автор: Gonzalez-Miranda J.M.

Аннотация:

"This book presents a comprehensive overview of the research and latest developments in the field of the dynamics of coupled and driven chaotic oscillators, aimed at a wide audience. Since 1990, there has been very active research devoted to the field, culminating in a considerable body of knowledge, while active research continues.

The results presented in the book will be valuable for scientific analysis and explanation in various different scientific disciplines, with potential applications in medicine and engineering. The contents include a selection of the most basic theoretical results, as well as experiments and applications presented at a mathematical level suited to readers working in non-hard sciences. It will also be of interest to physicists and mathematicians looking for an introduction to the field. "


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 224

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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