Theory of Chaos Control |
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1 | (20) |
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1 | (1) |
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A One-Dimensional Example |
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2 | (2) |
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Controlling Chaos in Two Dimensions |
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4 | (9) |
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Stabilizing a Fixed Point |
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5 | (6) |
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Stabilizing a Periodic Orbit of Higher Period |
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11 | (2) |
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Pole placement method of controlling chaos in high dimensions |
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13 | (3) |
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16 | (1) |
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17 | (4) |
Theory of Chaos Control |
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Principles of Time Delayed Feedback Control |
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21 | (22) |
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21 | (1) |
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Mechanism of delayed feedback control |
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22 | (5) |
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Limits of the simple feedback method |
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27 | (4) |
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Advanced control strategies |
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31 | (3) |
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Influence of a delay mismatch |
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34 | (4) |
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38 | (5) |
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Control of Patterns and Spatiotemporal Chaos and its Applications |
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43 | (44) |
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43 | (3) |
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Suppressing spatiotemporal chaos in CML systems |
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46 | (11) |
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Pattern control in one-way coupled CML systems |
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57 | (11) |
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Applications of pattern control and chaos synchronization in spatiotemporal systems |
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68 | (19) |
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Control of Spatially Extended Chaotic Systems |
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87 | (32) |
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87 | (2) |
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89 | (5) |
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89 | (1) |
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Symmetry, Locality and Pinning Control |
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90 | (2) |
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Periodic Array of Pinnings |
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92 | (2) |
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94 | (4) |
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Control in the Presence of Noise |
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98 | (3) |
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Control of Periodic Orbits |
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101 | (2) |
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103 | (4) |
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107 | (8) |
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107 | (1) |
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108 | (5) |
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113 | (2) |
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115 | (4) |
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Topological Defects and Control of Spatio-Temporal Chaos |
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119 | (22) |
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119 | (2) |
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Complex Ginzburg-Landau equation and its basic solutions |
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121 | (4) |
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Stability of Basic Solutions |
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125 | (4) |
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125 | (1) |
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Absolute versus Convective Instability of Traveling Waves |
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125 | (1) |
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Stability of topological defects in one and two dimensions |
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126 | (3) |
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Control of Chaos in the Complex Ginzburg-Landau Equation |
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129 | (5) |
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One-dimensional situation. Control of the hole solution |
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129 | (3) |
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Control of spiral in the two-dimensional complex complex Ginzburg-Landau Equation |
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132 | (2) |
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Control of Spatio-Temporal Chaos in Reaction-Diffusion Systems |
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134 | (2) |
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136 | (5) |
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Targeting in Chaotic Dynamical Systems |
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141 | (16) |
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141 | (1) |
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An Outline of Targeting Algorithms |
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142 | (6) |
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The Tree-Targeting Algorithm |
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148 | (2) |
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150 | (4) |
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154 | (3) |
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Using Chaotic Sensitivity |
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157 | (24) |
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157 | (2) |
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159 | (17) |
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159 | (1) |
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Using Chaotic Sensitivity |
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160 | (1) |
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Implementations: Lorenz Attractor |
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160 | (4) |
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Implementations: Higher Dimensionality |
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164 | (1) |
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165 | (2) |
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Why Search for Intersections? |
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167 | (2) |
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Effects of Noise and Modeling Errors |
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169 | (1) |
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Experimental verification |
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170 | (6) |
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176 | (5) |
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Controlling Transient Chaos on Chaotic Saddles |
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181 | (24) |
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181 | (1) |
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Properties of chaotic saddles |
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182 | (3) |
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The basic idea for controlling chaotic saddles |
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185 | (2) |
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Comparison with controlling permanent chaos |
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187 | (1) |
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188 | (1) |
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Controlling motion on fractal basin boundaries |
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189 | (1) |
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Controlling chaotic scattering |
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189 | (2) |
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An improved control of chaotic saddles |
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191 | (5) |
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196 | (9) |
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Periodic Orbit Theory for Classical Chaotic Systems |
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205 | (24) |
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205 | (1) |
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Strange repellers and cycle expansions |
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206 | (6) |
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Recycling measure of chaos |
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212 | (3) |
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Periodic orbit-theory of deterministic diffusion |
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215 | (4) |
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The inclusion of marginal fixed points |
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219 | (6) |
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225 | (4) |
Application of Chaos Control |
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Synchronization in Chaotic Systems, Concepts and Applications |
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229 | (42) |
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Introduction and Motivation |
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229 | (1) |
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The Geometry of Synchronization |
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230 | (2) |
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230 | (1) |
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Some Generalizations and a Definition of Identical Synchronization |
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231 | (1) |
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The Dynamics of Synchronization |
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232 | (7) |
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Stability and the Transverse Manifold |
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232 | (3) |
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Synchronizing Chaotic Systems, Variations on Themes |
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235 | (4) |
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Synchronous Circuits and Applications |
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239 | (6) |
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Stability and Bifurcations of Synchronized, Mutually Coupled Chaotic Systems |
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245 | (10) |
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Stability for Coupled, Chaotic Systems |
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245 | (2) |
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Coupling Thresholds for Synchronized Chaos and Bursting |
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247 | (2) |
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Desynchronization Thresholds at Increased Coupling |
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249 | (2) |
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Size Limits on Certain Chaotic Synchronized Arrays |
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251 | (1) |
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Riddled Basins of Synchronization |
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252 | (3) |
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Transformations, Synchronization, and Generalized Synchronization |
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255 | (16) |
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Synchronizing with Functions of the Dynamical Variables |
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256 | (1) |
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Hyperchaos Synchronization |
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257 | (2) |
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Generalized Synchronization |
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259 | (12) |
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Synchronization of Chaotic Systems |
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271 | (34) |
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271 | (3) |
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Synchronization of identical systems |
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274 | (4) |
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Constructing pairs of synchronizing systems |
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275 | (3) |
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Transversal instabilities and noise |
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278 | (3) |
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281 | (3) |
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Spatially extended systems |
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284 | (2) |
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Synchronization of nonidentical systems |
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286 | (7) |
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Generalized synchronization I |
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286 | (3) |
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Generalized synchronization II |
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289 | (1) |
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Non-identical synchronization of identical systems |
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290 | (2) |
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292 | (1) |
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Applications and Conclusion |
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293 | (12) |
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Phase Synchronization of Regular and Chaotic Oscillators |
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305 | (24) |
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305 | (1) |
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Synchronization of periodic oscillations |
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306 | (3) |
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Phase of a chaotic oscillator |
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309 | (3) |
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309 | (2) |
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Dynamics of the phase of chaotic oscillations |
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311 | (1) |
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Phase synchronization by external force |
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312 | (6) |
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312 | (1) |
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313 | (1) |
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Interpretation through embedded periodic orbits |
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314 | (4) |
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Phase synchronization in coupled systems |
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318 | (3) |
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Sychronization of two interacting oscillators |
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318 | (2) |
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Synchronization in a Population of Globally Coupled Chaotic Oscillators |
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320 | (1) |
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Lattice of chaotic oscillators |
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321 | (1) |
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Synchronization of space-time chaos |
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322 | (1) |
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Detecting synchronization in data |
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322 | (1) |
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323 | (6) |
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Tools for Detecting and Analyzing Generalized Synchronization of Chaos in Experiment |
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329 | (36) |
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329 | (2) |
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Generalized Synchronization of Chaos |
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331 | (1) |
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Weak and Strong Synchronization |
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332 | (7) |
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Properties of the Synchronization Manifold |
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332 | (2) |
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334 | (5) |
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339 | (5) |
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344 | (6) |
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Algorithm for Estimating CLEs |
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345 | (3) |
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348 | (2) |
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350 | (9) |
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One-Way Coupled Double-Scroll Oscillators |
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350 | (7) |
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Double-scroll Oscillator Driven with the Mackey-Glass System |
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357 | (2) |
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359 | (6) |
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Controlling Chaos in a Highdimensional Continuous Spatiotemporal Model |
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365 | (22) |
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365 | (1) |
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El Nino's dynamics and chaos |
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366 | (7) |
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367 | (1) |
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368 | (3) |
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371 | (2) |
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Choosing a control variable and a control point in space |
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373 | (2) |
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A continuous delay-coordinates phase space approach to controlling chaos in high dimensional, spatiotemporal systems |
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375 | (2) |
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Controllability of delay-coordinate phase space points along an unstable periodic orbit |
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377 | (1) |
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378 | (3) |
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Using non-delay coordinates for phase space reconstruction |
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381 | (2) |
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383 | (4) |
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Controlling Production Lines |
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387 | (18) |
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387 | (2) |
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TSS Production Lines and Their Model |
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389 | (3) |
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392 | (7) |
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A Self-Organized Order Picking System for a Warehouse |
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399 | (2) |
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401 | (1) |
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401 | (4) |
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Chaos Control in Biological Networks |
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405 | (22) |
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405 | (1) |
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Control of a delay differential equation |
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406 | (2) |
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Control of chaos in a network of oscillators |
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408 | (3) |
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408 | (3) |
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411 | (7) |
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Static pattern discrimination |
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415 | (1) |
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415 | (1) |
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416 | (2) |
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Chaos control in biological neural networks |
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418 | (3) |
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421 | (3) |
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424 | (3) |
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Chaos Control in Biological Systems |
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427 | (32) |
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427 | (1) |
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428 | (8) |
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Introduction to ventricular fibrillation |
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428 | (1) |
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Fibrillation as a dynamical state |
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428 | (1) |
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Detection of deterministic dynamics in canine ventricular fibrillation |
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429 | (2) |
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Imaging of the spatiotemporal evolution of ventricular fibrillation |
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431 | (5) |
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Control of Chaos in Cardiac Systems |
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436 | (12) |
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Control of isolated cardiac tissue |
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436 | (5) |
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Control of atrial fibrillation in humans |
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441 | (7) |
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Control of Chaos in Brain Tissue |
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448 | (1) |
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DC Field Interactions with Mammalian Neuronal Tissue |
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448 | (5) |
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453 | (6) |
Experimental Control of Chaos |
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Experimental Control of Chaos in Electronic Circuits |
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459 | (28) |
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459 | (1) |
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460 | (8) |
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464 | (1) |
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Controlling the Diode Resonator |
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464 | (4) |
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Controlling Coupled Diode Resonators |
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468 | (5) |
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On Higher Dimensional Control |
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470 | (3) |
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Controlling Spatiotemporal Chaos |
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473 | (10) |
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475 | (1) |
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The Diode Resonator Open Flow System |
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476 | (1) |
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477 | (6) |
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483 | (4) |
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487 | (26) |
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487 | (1) |
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488 | (5) |
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The single mode class B laser |
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488 | (2) |
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Class B lasers with modulated parameters |
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490 | (1) |
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CO2 laser with electronic feedback |
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491 | (1) |
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Class B lasers with saturable absorber |
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491 | (1) |
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Multimode class B lasers with intracavity second harmonic generation |
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492 | (1) |
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Class B lasers in presence of feedback |
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493 | (1) |
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Feedback methods of controlling chaos |
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493 | (7) |
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Basic ingredients of chaos control |
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493 | (2) |
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Experimental implementation of control |
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495 | (4) |
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Delayed feedback control of chaos |
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499 | (1) |
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Stabilization of unstable steady states |
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500 | (3) |
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Nonfeedback control of chaos |
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503 | (2) |
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Invasive vs nonivasive methods |
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503 | (1) |
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503 | (2) |
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Applications of Controlling Laser Chaos |
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505 | (3) |
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Enlargement of the range of cw operation |
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506 | (1) |
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Floquet multipliers and manifold connections |
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506 | (2) |
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508 | (5) |
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Control of Chaos in Plasmas |
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513 | (50) |
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513 | (1) |
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514 | (9) |
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Overview over Common Chaos Control Schemes |
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514 | (2) |
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516 | (2) |
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518 | (5) |
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523 | (16) |
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524 | (7) |
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531 | (8) |
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539 | (11) |
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539 | (2) |
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Experiment and Transition to Chaos |
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541 | (2) |
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Control of Ionization Wave Chaos |
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543 | (7) |
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550 | (4) |
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554 | (9) |
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Chaos Control in Spin Systems |
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563 | (28) |
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563 | (2) |
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Ferromagnetic Resonance in Spin-Wave Instabilities |
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565 | (4) |
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565 | (1) |
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566 | (1) |
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567 | (2) |
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Nonresonant Parametric Modulation |
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569 | (5) |
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Analytical and Numerical Approach |
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569 | (2) |
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Experimental Suppression of Spin-Wave Chaos |
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571 | (3) |
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Occassional Proportional Feedback |
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574 | (4) |
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574 | (2) |
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Experimental Control by an Analog Feedback Device |
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576 | (2) |
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Time-Delayed Feedback Control |
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578 | (7) |
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578 | (5) |
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Application to Spin-Wave Chaos |
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583 | (2) |
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585 | (6) |
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Control of Chemical Waves in Excitable Media by External Perturbation |
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591 | (24) |
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591 | (1) |
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Spiral Waves and the Belousov-Zhabotinsky Reaction |
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592 | (4) |
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596 | (14) |
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Chemical Parameters and Oxygen-Inhibition |
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596 | (2) |
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Control by Electric Fields |
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598 | (5) |
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603 | (7) |
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610 | (5) |
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Predictability and Local Control of Low-dimensional chaos |
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615 | (30) |
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615 | (1) |
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A definition of predictability |
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616 | (2) |
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Effective Lyapunov exponents |
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618 | (5) |
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623 | (1) |
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The origin of predictability contours |
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624 | (5) |
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Chaos control in the presence of large effective Lyapunov exponents |
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629 | (5) |
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The local entropy algorithm |
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630 | (1) |
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631 | (3) |
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Adaptive orbit correction in chaos control |
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634 | (11) |
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Orbit corrections in the Henon map |
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635 | (1) |
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Orbit corrections in a changing environment |
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636 | (1) |
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Experimental orbit correction at the driven pendulum |
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637 | (1) |
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Interaction of prediction and control, outlook |
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638 | (7) |
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Experimental Control of Highly Unstable Systems Using Time Delay Coordinates |
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645 | (42) |
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645 | (3) |
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648 | (1) |
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Extensions of the OGY-control method |
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649 | (5) |
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Quasicontinuous control for highly unstable systems |
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649 | (3) |
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The OGY control method for time delay coordinates |
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652 | (2) |
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Quasicontinuous control using time delay coordinates |
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654 | (5) |
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Local dynamics in the time delay embedding system |
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654 | (2) |
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Quasicontinuous control formula for time delay coordinates |
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656 | (3) |
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The bronze ribbon - Experimental setup |
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659 | (3) |
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Control vectors from scalar measurements |
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662 | (10) |
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Unstable periodic orbits from recurrent points |
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663 | (1) |
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Linear dynamics of the unperturbed system |
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663 | (5) |
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Dependence on the control parameter |
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668 | (1) |
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The adaptive orbit correction |
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669 | (3) |
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Control experiments - The bronze ribbon |
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672 | (8) |
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Quasicontinuous control of the bronze ribbon with time delay coordinates |
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672 | (3) |
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Tracking of the bronze ribbon experiment |
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675 | (5) |
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680 | (7) |
Index |
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687 | |