Handbook of chaos control:
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| Previous Title: | Handbook of chaos control / Heinz Georg Schuster |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2008
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| Edition: | 2., completely rev. and enl. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXX, 819 S. Ill., zahlr. graph. Darst. |
| ISBN: | 9783527406050 3527406050 |
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| 245 | 1 | 0 | |a Handbook of chaos control |c ed. by Eckehard Schöll ... |
| 250 | |a 2., completely rev. and enl. ed. | ||
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| 650 | 4 | |a Nonlinear control theory | |
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HANDBOOK OF CHAOS CONTROL EDITED BY ECKEHARD SCHOLL AND HEINZ GEORG
SCHUSTER 2 ND , COMPLETELY REVISED AND ENLARGED EDITION WILEY- VCH
WILEY-VCH VERLAG GMBH & CO. KGAA CONTENTS PREFACE XXI LIST OF
CONTRIBUTORS XXIII PART I BASIC ASPECTS AND EXTENSION OF METHODS 1
CONTROLLING CHAOS 3 ELBERT E. N. MACAU AND CELSO CREBOGI 1.1
INTRODUCTION 3 1.2 THE OGY CHAOS CONTROL 6 1.3 TARGETING-STEERING
CHAOTIC TRAJECTORIES 8 1.3.1 PART I: FINDING A PROPER TRAJECTORY 9 1.3.2
PART II: FINDING A PSEUDO-ORBIT TRAJECTORY 10 1.3.3 THE TARGETING
ALGORITHM 12 1.4 APPLYING CONTROL OF CHAOS AND TARGETING IDEAS 1.4.1
CONTROLLING AN ELECTRONIC CIRCUIT 13 1.4.2 CONTROLLING A COMPLEX SYSTEM
19 1.5 CONCLUSION 26 REFERENCES 26 2 TIME-DELAY CONTROL FOR DISCRETE
MAPS 29 JOSHUA E. S. SOCOLAR 2.1 OVERVIEW: WHY STUDY DISCRETE MAPS? 29
2.2 THEME AND VARIATIONS 31 2.2.1 RUDIMENTARY TIME-DELAY FEEDBACK 32
2.2.2 EXTENDING THE DOMAIN OF CONTROL 34 2.2.3 HIGH-DIMENSIONAL SYSTEMS
37 2.3 ROBUSTNESS OF TIME-DELAY STABILIZATION 41 2.4 SUMMARY 44
ACKNOWLEDGMENTS 44 REFERENCES 44 HANDBOOK OF CHAOS CONTROL, 2ND ED.
EDITED BY E. SCHOLL AND H. G. SCHUSTER COPYRIGHT 2008 WILEY-VCH VERLAG
GMBH & CO. KGAA, WEINHEIM ISBN: 978-3-527-40605-0 CONTENTS 3 AN
ANALYTICAL TREATMENT OF THE DELAYED FEEDBACK CONTROL ALGORITHM 47
KESTUTIS PYRAGAS, TATJANA PYRAGIENE, AND VIKTORAS PYRAGAS 3.1
INTRODUCTION 47 3.2 PROPORTIONAL VERSUS DELAYED FEEDBACK 50 3.3
CONTROLLING PERIODIC ORBITS ARISING FROM A PERIOD DOUBLING BIFURCATION
53 3.3.1 EXAMPLE: CONTROLLING THE ROESSLER SYSTEM 54 3.4 CONTROL OF
FORCED SELF-SUSTAINED OSCILLATIONS 57 3.4.1 PROBLEM FORMULATION AND
AVERAGED EQUATION 57 3.4.2 PERIODIC ORBITS OF THE FREE SYSTEM 58 3.4.3
LINEAR STABILITY OF THE SYSTEM CONTROUED BY DELAYED FEEDBACK 3.4.4
NUMERICAL DEMONSTRATIONS 63 3.5 CONTROLLING TORSION-FREE PERIODIC ORBITS
63 3.5.1 EXAMPLE: CONTROLLING THE LORENZ SYSTEM AT A SUBCRITICAL HOPF
BIFURCATION 65 3.6 CONCLUSIONS 68 REFERENCES 70 4 BEYOND THE ODD-NUMBER
LIMITATION OF TIME-DELAYED FEEDBACK CONTROL 73 BERNOLD FIEDLER, VALENTIN
FLUNKERT, MARC CEORGI, PHILIPP HAVEL, AND ECKEHARD SCHOLL 4.1
INTRODUCTION 73 4.2 MECHANISM OF STABILIZATION 74 4.3 CONDITIONS ON THE
FEEDBACK GAIN 78 4.4 CONCLUSION 82 ACKNOWLEDGMENTS 82 APPENDIX:
CALCULATION OF FLOQUET EXPONENTS 82 REFERENCES 83 5 ON GLOBAL PROPERTIES
OF TIME-DELAYED FEEDBACK CONTROL 85 WOLFRAM JUST 5.1 INTRODUCTION 85 5.2
A COMMENT ON CONTROL AND ROOT FINDING ALGORITHMS 88 5.3 CODIMENSION-TWO
BIFURCATIONS AND BASINS OF ATTRACTION 91 5.3.1 THE TRANSITION FROM
SUPER- TO SUBCRITICAL BEHAVIOR 91 5.3.2 PROBING BASINS OF ATTRACTION IN
EXPERIMENTS 93 5.4 A CASE STUDY OF GLOBAL FEATURES FOR TIME-DELAYED
FEEDBACK CONTROL 94 5.4.1 ANALYTICAL BIFURCATION ANALYSIS OF
ONE-DIMENSIONAL MAPS 95 5.4.2 DEPENDENCE OF SUB- AND SUPERCRITICAL
BEHAVIOR ON THE OBSERVABLE 98 5.4.3 INFLUENCE OF THE COUPLING OF THE
CONTROL FORCE 99 5.5 CONCLUSION 101 CONTENTS VII ACKNOWLEDGMENTS , 102
APPENDIX A. NORMAL FORM REDUCTION 103 APPENDIX B. SUPER- AND SUBCRITICAL
HOPF BIFURCATION FOR MAPS 106 REFERENCES 106 6 POINCARE-BASED CONTROL OF
DELAYED MEASURED SYSTEMS: LIMITATIONS AND IMPROVED CONTROL 109 JENS
CHRISTIAN CLAUSSEN 6.1 INTRODUCTION 109 6.1.1 THE DELAY
PROBLEM-TIME-DISCRETE CASE 109 6.1.2 EXPERIMENTAL SETUPS WITH DELAY 111
6.2 OTT-GREBOGI-YORKE (OGY) CONTROL 112 6.3 LIMITATIONS OF UNMODIFIED
CONTROL AND SIMPLE IMPROVED CONTROL SCHEINES 113 6.3.1 LIMITATIONS OF
UNMODIFIED OGY CONTROL IN THE PRESENCE OF DELAY 113 6.3.2 STABILITY
DIAGRAMS DERIVED BY THE JURY CRITERION 116 6.3.3 STABILIZING UNKNOWN
FIXED POINTS: LIMITATIONS OF UNMODIFIED DIFFERENCE CONTROL 116 6.3.4
RHYTHMIC CONTROL SCHEMES: RHYTHMIC OGY CONTROL 119 6.3.5 RHYTHMIC
DIFFERENCE CONTROL 120 6.3.6 A SIMPLE MEMORY CONTROL SCHEME: USING STATE
SPACE MEMORY 122 6.4 OPTIMAL IMPROVED CONTROL SCHEMES 123 6.4.1 LINEAR
PREDICTIVE LOGGING CONTROL (LPLC) 123 6.4.2 NONLINEAR PREDICTIVE LOGGING
CONTROL 124 6.4.3 STABILIZATION OF UNKNOWN FIXED POINTS: MEMORY
DIFFERENCE CONTROL (MDC) 125 6.5 SUMMARY 126 REFERENCES 127 7 NONLINEAR
AND ADAPTIVE CONTROL OF CHAOS 129 ALEXANDER FRADKOV AND ALEXANDER
POGROMSKY 7.1 INTRODUCTION 129 7.2 CHAOS AND CONTROL: PRELIMINARIES 130
7.2.1 DEFINITIONS OF CHAOS 130 7.2.2 MODELS OF CONTROLLED SYSTEMS 131
7.2.3 CONTROL GOALS 132 7.3 METHODS OF NONLINEAR CONTROL 134 7.3.1
GRADIENT METHOD 135 7.3.2 SPEED-GRADIENT METHOD 136 7.3.3 FEEDBACK
LINEARIZATION 141 7.3.4 OTHER METHODS 142 7.3.5 GRADIENT CONTROL OF THE
HENON SYSTEM 144 7.3.6 FEEDBACK LINEARIZATION CONTROL OF THE LORENZ
SYSTEM 146 VIII CONTENTS 7.3.7 SPEED-GRADIENT STABILIZATION OF THE
EQUILIBRIUM POINT FOR THE THERMAL CONVECTION LOOP MODEL 147 7.4 ADAPTIVE
CONTROL 148 7.4.1 GENERAL DEFINITIONS 148 7.4.2 ADAPTIVE MASTER-SLAVE
SYNCHRONIZATION OF ROESSLER SYSTEMS 149 7.5 OTHER PROBLEMS 154 7.6
CONCLUSIONS 155 ACKNOWLEDGMENT 155 REFERENCES 156 PART II CONTROLLING
SPACE-TIME CHAOS 8 LOCALIZED CONTROL OF SPATIOTEMPORAL CHAOS 161 ROMAN
O. CRIGORIEV AND ANDREAS HANDEL 8.1 INTRODUCTION 161 8.1.1 EMPIRICAL
CONTROL 163 8.1.2 MODEL-BASED CONTROL 164 8.2 SYMMETRY AND THE MINIMAL
NUMBER OF SENSORS/ACTUATORS 167 8.3 NONNORMALITY AND NOISE AMPLIFICATION
170 8.4 NONLINEARITY AND THE CRITICAL NOISE LEVEL 175 8.5 CONCLUSIONS
177 REFERENCES 177 9 CONTROLLING SPATIOTEMPORAL CHAOS: THE PARADIGM OF
THE COMPLEX GINZBURG-LANDAU EQUATION 181 STEFANO BOCCALETTI AND JEAN
BRAGARD 9.1 INTRODUCTION 181 9.2 THE COMPLEX GINZBURG-LANDAU EQUATION
183 9.2.1 DYNAMICS CHARACTERIZATION 185 9.3 CONTROL OF THE CGLE 187 9.4
CONCLUSIONS AND PERSPECTIVES 192 ACKNOWLEDGMENT 193 REFERENCES 193 10
MULTIPLE DELAY FEEDBACK CONTROL 197 ALEXANDER AHLBORN AND ULRICH PARLITZ
10.1 INTRODUCTION 197 10.2 MULTIPLE DELAY FEEDBACK CONTROL 198 10.2.1
LINEAR STABILITY ANALYSIS 199 10.2.2 EXAMPLE: COLPITTS OSCILLATOR 200
10.2.3 COMPARISON WITH HIGH-PASS FILTER AND PD CONTROLLER 203 10.2.4
TRANSFER FUNCTION OFMDFC 204 10.3 FROM MULTIPLE DELAY FEEDBACK CONTROL
TO NOTCH FILTER FEEDBACK 206 10.4 CONTROLLABILITY CRITERIA 208 10.4.1
MULTIPLE DELAY FEEDBACK CONTROL 209 10.4.2 NOTCH FILTER FEEDBACK AND
HIGH-PASS FILTER 210 10.5 LASER STABILIZATION USING MDFC AND NFF 211
10.6 CONTROLLING SPATIOTEMPORAL CHAOS 213 10.6.1 THE GINZBURG-LANDAU
EQUATION 213 10.6.2 CONTROLLING TRAVELING PLANE WAVES 214 10.6.3 LOCAL
FEEDBACK CONTROL 215 10.7 CONCLUSION 218 REFERENCES 219 PART III
CONTROLLING NOISY MOTION 11 CONTROL OF NOISE-INDUCED DYNAMICS 223
NATALIA B. JANSON, ALEXANDER C. BALANOV, AND ECKEHARD SCHOLL 11.1
INTRODUCTION 223 11.2 NOISE-INDUCED OSCILLATIONS BELOW ANDRONOV-HOPF
BIFURCATION AND THEIR CONTROL 226 11.2.1 WEAK NOISE AND CONTROL:
CORRELATION FUNCTION 228 11.2.2 WEAK NOISE AND NO CONTROL: CORRELATION
TIME AND SPECTRUM 229 11.2.3 WEAK NOISE AND CONTROL: CORRELATION TIME
231 11. 2 .4 WEAK NOISE AND CONTROL: SPECTRUM 235 11.2.5 ANY NOISE AND
NO CONTROL: CORRELATION TIME 236 11.2.6 ANY NOISE AND CONTROL:
CORRELATION TIME AND SPECTRUM 238 11.2.7 SO, WHAT CAN WE CONTROL? 240
11.3 NOISE-INDUCED OSCILLATIONS IN AN EXCITABLE SYSTEM AND THEIR CONTROL
241 11.3.1 COHERENCE RESONANCE IN THE FITZHUGH-NAGUMO SYSTEM 243 11.3.2
CORRELATION TIME AND SPECTRUM WHEN FEEDBACK IS APPLIED 244 11.3.3
CONTROL OF SYNCHRONIZATION IN COUPLED FITZHUGH-NAGUMO SYSTEMS 245 11.3.4
WHAT CAN WE CONTROL IN AN EXCITABLE SYSTEM? 246 11.4 DELAYED FEEDBACK
CONTROL OF NOISE-INDUCED PULSES IN A MODEL OF AN EXCITABLE MEDIUM 247
11.4.1 MODEL DESCRIPTION 247 11.4.2 CHARACTERISTICS OF NOISE-INDUCED
PATTERNS 249 11.4.3 CONTROL OF NOISE-INDUCED PATTERNS 251 11.4.4
MECHANISMS OF DELAYED FEEDBACK CONTROL OF THE EXCITABLE MEDIUM 253
11.4.5 WHAT CAN BE CONTROLLED IN AN EXCITABLE MEDIUM? 254 11.5 DELAYED
FEEDBACK CONTROL OF NOISE-INDUCED PATTERNS IN A GLOBALLY COUPLED
REACTION-DIFFUSION MODEL 255 11.5.1 SPATIOTEMPORAL DYNAMICS IN THE
UNCONTROLLED DETERMINISTIC SYSTEM 256 11.5.2 NOISE-INDUCED PATTERNS IN
THE UNCONTROLLED SYSTEM 258 11.5.3 TIME-DELAYED FEEDBACK CONTROL OF
NOISE-INDUCED PATTERNS 260 11.5.4 LINEAR MODES OF THE INHOMOGENEOUS
FIXED POINT 264 11.5.5 DELAY-INDUCED OSCILLATORY PATTERNS 268 11.5.6
WHAT CAN BE CONTROUED IN A GLOBALLY COUPLED REACTION-DIFFUSION SYSTEM?
269 11.6 SUMMARY AND CONCLUSIONS 270 ACKNOWLEDGMENTS 270 REFERENCES 270
12 CONTROLLING COHERENCE OF NOISY AND CHAOTIC OSCILLATORS BY DELAYED
FEEDBACK 275 DENIS COLDOBIN, MICHAEL ROSENBLUM, AND ARKADY PIKOVSKY 12.1
CONTROL OF COHERENCE: NUMERICAL RESULTS 276 12.1.1 NOISY OSCILLATOR 276
12.1.2 CHAOTIC OSCILLATOR 277 12.1.3 ENHANCING PHASE SYNCHRONIZATION 279
12.2 THEORY OF COHERENCE CONTROL 279 12.2.1 BASIC PHASE MODEL 279 12.2.2
NOISE-FREE CASE 280 12.2.3 GAUSSIAN APPROXIMATION 280 12.2.4
SELF-CONSISTENT EQUATION FOR DIFFUSION CONSTANT 282 12.2.5 COMPARISON OF
THEORY AND NUMERICS 283 12.3 CONTROL OF COHERENCE BY MULTIPLE DELAYED
FEEDBACK 283 12.4 CONCLUSION 288 REFERENCES 289 13 RESONANCES INDUCED BY
THE DELAY TIME IN NONLINEAR AUTONOMOUS OSCILLATORS WITH FEEDBACK 291
CRISTINA MASOLLER ACKNOWLEDGMENT 298 REFERENCES 299 PART IV
COMMUNICATING WITH CHAOS, CHAOS SYNCHRONIZATION 14 SECURE COMMUNICATION
WITH CHAOS SYNCHRONIZATION 303 WOLFGANG KINZEL AND IDO KANTER 14.1
INTRODUCTION 303 14.2 SYNCHRONIZATION OF CHAOTIC SYSTEMS 304 14.3 CODING
AND DECODING SECRET MESSAGES IN CHAOTIC SIGNALS 309 14 .4 ANALYSIS OF
THE EXCHANGED SIGNAL 311 14.5 NEURAL CRYPTOGRAPHY 313 14.6 PUBLIC KEY
EXCHANGE BY MUTUAL SYNCHRONIZATION 315 14.7 PUBLIC KEYS BY ASYMMETRIE
ATTRACTORS 318 14.8 MUTUAL CHAOS PASS FILTER 319 14.9 DISCUSSION 321
REFERENCES 323 15 NOISE ROBUST CHAOTIC SYSTEMS 325 THOMAS L CARROLL 15.1
INTRODUCTION 325 15.2 CHAOTIC SYNCHRONIZATION 326 15.3 2-FREQUENCY
SELF-SYNCHRONIZING CHAOTIC SYSTEMS 326 15.3.1 SIMPLE MAPS 326 15.4
2-FREQUENCY SYNCHRONIZATION IN FLOWS 329 15.4.1 2-FREQUENCY ADDITIVE
ROESSLER 329 15.4.2 PARAMETER VARIATION AND PERIODIC ORBITS 332 15.4.3
UNSTABLE PERIODIC ORBITS 333 15.4.4 FLOQUET MULTIPLIERS 334 15.4.5
LINEWIDTHS 335 15.5 CIRCUIT EXPERIMENTS 336 15.5.1 NOISE EFFECTS 338
15.6 COMMUNICATION SIMULATIONS 338 15.7 MULTIPLICATIVE TWO-FREQUENCY
ROESSLER CIRCUIT 341 15.8 CONCLUSIONS 346 REFERENCES 346 16 NONLINEAR
COMMUNICATION STRATEGIES 349 HENRY D. I. ABARBANEL 16.1 INTRODUCTION 349
16.1.1 SECRECY, ENCRYPTION, AND SECURITY? 350 16.2 SYNCHRONIZATION 351
16.3 COMMUNICATING USING CHAOTIC CARRIERS 353 16.4 TWO EXAMPLES FROM
OPTICAL COMMUNICATION 355 16.4.1 RARE-EARTH-DOPED FIBER AMPLIFIER LASER
355 16.4.2 TIME DELAY OPTOELECTRONIC FEEDBACK SEMICONDUCTOR LASER 357
16.5 CHAOTIC PULSE POSITION COMMUNICATION 359 16.6 WHY USE CHAOTIC
SIGNALS AT ALL? 362 16.7 UNDISTORTING THE NONLINEAR EFFECTS OF THE
COMMUNICATION CHANNEL 363 16.8 CONCLUSIONS 366 REFERENCES 367 17
SYNCHRONIZATION AND MESSAGE TRANSMISSION FOR NETWORKED CHAOTIC OPTICAL
COMMUNICATIONS 369 K. ALAN SHORE, PAUL S. SPENCER, AND LLESTYN PIERCE
17.1 INTRODUCTION 369 17.2 SYNCHRONIZATION AND MESSAGE TRANSMISSION 370
17.3 NETWORKED CHAOTIC OPTICAL COMMUNICATION 372 17.3.1 CHAOS
MULTIPLEXING 373 17.3.2 MESSAGE RELAY 373 17.3.3 MESSAGE BROADCASTING
374 XII CONTENTS 17.4 SUMMARY 376 ACKNOWLEDGMENTS 376 REFERENCES 376 18
FEEDBACK CONTROL PRINCIPLES FOR PHASE SYNCHRONIZATION 379 VLADIMIR N.
BELYKH, CRIGORY V. OSIPOV, AND JUERGEN KURTHS 18.1 INTRODUCTION 379 18.2
GENERAL PRINCIPLES OF AUTOMATIC SYNCHRONIZATION 381 18.3 TWO COUPLED
POINCARE SYSTEMS 384 18.4 COUPLED VAN DER POL AND ROESSLER OSCILLATORS
386 18.5 TWO COUPLED ROESSLER OSCILLATORS 389 18.6 COUPLED ROESSLER AND
LORENZ OSCILLATORS 391 18.7 PRINCIPLES OF AUTOMATIC SYNCHRONIZATION IN
NETWORKS OF COUPLED OSCILLATORS 393 18.8 SYNCHRONIZATION OF LOCALLY
COUPLED REGULAER OSCILLATORS 395 18.9 SYNCHRONIZATION OF LOCALLY COUPLED
CHAOTIC OSCILLATORS 397 18.10 SYNCHRONIZATION OF GLOBALLY COUPLED
CHAOTIC OSCILLATORS 399 18.11 CONCLUSIONS 401 REFERENCES 401 PART V
APPLICATIONS TO OPTICS 19 CONTROLLING FAST CHAOS IN OPTOELECTRONIC DELAY
DYNAMICAL SYSTEMS 407 LUCAS LLLING, DANIEL J. CAUTHIER, AND JONATHAN N.
BLAKELY 19.1 INTRODUCTION 407 19.2 CONTROL-LOOP LATENCY: A SIMPLE
EXAMPLE 408 19.3 CONTROLLING FAST SYSTEMS 412 19.4 A FAST OPTOELECTRONIC
CHAOS GENERATOR 415 19.5 CONTROLLING THE FAST OPTOELECTRONIC DEVICE 419
19.6 OUTLOOK 423 ACKNOWLEDGMENT 424 REFERENCES 424 20 CONTROL OF
BROAD-AREA LASER DYNAMICS WITH DELAYED OPTICAL FEEDBACK 427 NICOLETA
CACIU, EDELTRAUD GEHRIG, AND ORTWIN HESS 20.1 INTRODUCTION:
SPATIOTEMPORALLY CHAOTIC SEMICONDUCTOR LASERS 427 20.2 THEORY: TWO-LEVEL
MAXWELL-BLOCH EQUATIONS 429 20.3 DYNAMICS OF THE SOLITARY LASER 432 20.4
DETECTION OF SPATIOTEMPORAL COMPLEXITY 433 20.4.1 REDUCTION OF THE
NUMBER OF MODES BY COHERENT INJECTION 433 20.4.2 PULSE-INDUCED MODE
SYNCHRONIZATION 435 20.5 SELF-INDUCED STABILIZATION AND CONTROL WITH
DELAYED OPTICAL FEEDBACK 438 CONTENTS XII I 20.5.1 INFLUENCE OF DELAYED
OPTICAL FEEDBACK 439 20.5.2 INFLUENCE OF THE DELAY TIME 440 20.5.3
SPATIALLY STRUCTURED DELAYED OPTICAL FEEDBACK CONTROL 444 20.5.4
FILTERED SPATIALLY STRUCTURED DELAYED OPTICAL FEEDBACK 449 20.6
CONCLUSIONS 451 REFERENCES 453 21 NONINVASIVE CONTROL OF SEMICONDUCTOR
LASERS BY DELAYED OPTICAL FEEDBACK 455 HANS-JUERGEN WUENSCHE, SYLVIA
SCHIKORA, AND FRITZ HENNEBERGER 21.1 THE ROLE OF THE OPTICAL PHASE 456
21.2 GENERIC LINEAR MODEL 459 21.3 GENERALIZED LANG-KOBAYASHI MODEL 461
21.4 EXPERIMENT 462 21.4.1 THE INTEGRATED TANDEM LASER 463 21.4.2 DESIGN
OF THE CONTROL CAVITY 464 21.4.3 MAINTAINING RESONANCE 465 21.4.4
LATENCY AND COUPLING STRENGTH 465 21.4.5 RESULTS OF THE CONTROL
EXPERIMENT 466 21.5 NUMERICAL SIMULATION 468 21.5.1 TRAVELING-WAVE MODEL
468 21.5.2 NONINVASIVE CONTROL BEYOND A HOPF BIFURCATION 470 21.5.3
CONTROL DYNAMICS 470 21.5.4 VARIATION OF THE CONTROL PARAMETERS 471 21.6
CONCLUSIONS 473 ACKNOWLEDGMENT 473 REFERENCES 473 22 CHAOS AND CONTROL
IN SEMICONDUCTOR LASERS 475 JUNJI OHTSUBO 22.1 INTRODUCTION 475 22.2
CHAOS IN SEMICONDUCTOR LASERS 476 22.2.1 LASER CHAOS 476 22.2.2 OPTICAL
FEEDBACK EFFECTS IN SEMICONDUCTOR LASERS 478 22.2.3 CHAOTIC EFFECTS IN
NEWLY DEVELOPED SEMICONDUCTOR LASERS 480 22.3 CHAOS CONTROL IN
SEMICONDUCTOR LASERS 485 22.4 CONTROL IN NEWLY DEVELOPED SEMICONDUCTOR
LASERS 494 22.5 CONCLUSIONS 497 REFERENCES 498 XIV CONTENTS 23 FROM
PATTERN CONTROL TO SYNCHRONIZATION: CONTROL TECHNIQUES IN NONLINEAR
OPTICAL FEEDBACK SYSTEMS 501 BJOERN GUETLICH AND CORNELIA DENZ 23.1
CONTROL METHODS FOR SPATIOTEMPORAL SYSTEMS 502 23.2 OPTICAL
SINGLE-FEEDBACK SYSTEMS 503 23.2.1 A SIMPLIFIED SINGLE-FEEDBACK MODEL
SYSTEM 504 23.2.2 THE PHOTOREFRACTIVE SINGLE-FEEDBACK SYSTEM - COHERENT
NONLINEARITY 506 23.2.3 THEORETICAL DESCRIPTION OF THE PHOTOREFRACTIVE
SINGLE-FEEDBACK SYSTEM 508 23.2.4 LINEAR STABILITY ANALYSIS 509 23.2.5
THE LCLV SINGLE-FEEDBACK SYSTEM - INCOHERENT NONLINEARITY 510 23.2.6
PHASE-ONLY MODE 511 23.2.7 POLARIZATION MODE 513 23.2.8 DISSIPATIVE
SOLITONS IN THE LCLV FEEDBACK SYSTEM 513 23.3 SPATIAL FOURIER CONTROL
514 23.3.1 EXPERIMENTAL DETERMINATION OF MARGINAL INSTABILITY 516 23.3.2
STABILIZATION OF UNSTABLE PATTERN 517 23.3.3 DIRECT FOURIER FILTERING
518 23.3.4 POSITIVE FOURIER CONTROL 518 23.3.5 NONINVASIVE FOURIER
CONTROL 519 23.4 REAL-SPACE CONTROL 520 23.4.1 INVASIVE FORCING 520
23.4.2 POSITIONING OF LOCALIZED STATES 522 23.4.3 SYSTEM HOMOGENIZATION
522 23.4.4 STATIC POSITIONING 523 23.4.5 ADDRESSING AND DYNAMIC
POSITIONING 523 23.5 SPATIOTEMPORAL SYNCHRONIZATION 524 23.5.1 SPATIAL
SYNCHRONIZATION OF PERIODIC PATTERN 524 23.5.2 UNIDIRECTIONAL
SYNCHRONIZATION OF TWO LCLV SYSTEMS 525 23.5.3 SYNCHRONIZATION OF
SPATIOTEMPORAL COMPLEXITY 526 23.6 CONCLUSIONS AND OUTLOOK 527
REFERENCES 528 PART VI APPLICATIONS TO ELECTRONIC SYSTEMS 24
DELAYED-FEEDBACK CONTROL OF CHAOTIC SPATIOTEMPORAL PATTERNS IN
SEMICONDUCTOR NANOSTRUCTURES 533 ECKEHARD SCHOLL 24.1 INTRODUCTION 533
24.2 CONTROL OF CHAOTIC DOMAIN AND FRONT PATTERNS IN SUPERLATTICES 536
24.3 CONTROL OF CHAOTIC SPATIOTEMPORAL OSCILLATIONS IN RESONANT
TUNNELING DIODES 544 24.4 CONCLUSIONS 553 ACKNOWLEDGMENTS 554 REFERENCES
554 25 OBSERVING GLOBAL PROPERTIES OF TIME-DELAYED FEEDBACK CONTROL IN
ELECTRONIC CIRCUITS 559 HARTMUT BENINER, CHOL-UNG CHOE, KLAUS HOEHNE,
CLEMENS VON LOEWENICH, HIROYUKI SHIRAHAMA, AND WOLFRAM JUST 25.1
INTRODUCTION 559 25.2 DISCONTINUOUS TRANSITIONS FOR EXTENDED
TIME-DELAYED FEEDBACK CONTROL 560 25.2.1 THEORETICAL CONSIDERATIONS 560
25.2.2 EXPERIMENTAL SETUP 561 25.2.3 OBSERVATION OF BISTABILITY 562
25.2.4 BASIN OF ATTRACTION 564 25.3 CONTROLLING TORSION-FREE UNSTABLE
ORBITS 565 25.3.1 APPLYING THE CONCEPT OF AN UNSTABLE CONTROLLER 567
25.3.2 EXPERIMENTAL DESIGN OF AN UNSTABLE VAN DER POL OSCILLATOR 567
25.3.3 CONTROL COUPLING AND BASIN OF ATTRACTION 569 25.4 CONCLUSIONS 572
REFERENCES 573 26 APPLICATION OF A BLACK BOX STRATEGY TO CONTROL CHAOS
575 ACHIM KITTEL AND MARTIN POPP 26.1 INTRODUCTION 575 26.2 THE MODEL
SYSTEMS 575 26.2.1 SHINRIKI OSCILLATOR 576 26.2.2 MACKEY-GLASS TYPE
OSCILLATOR 577 26.3 THE CONTROLLER 580 26.4 RESULTS OF THE APPLICATION
OF THE CONTROLLER TO THE SHINRIKI OSCILLATOR 582 26.4.1 SPECTROSCOPY OF
UNSTABLE PERIODIC ORBITS 584 26.5 RESULTS OF THE APPLICATION OF THE
CONTROLLER TO THE MACKEY-GLASS OSCILLATOR 585 26.5.1 SPECTROSCOPY OF
UNSTABLE PERIODIC ORBITS 587 26.6 FURTHER IMPROVEMENTS 589 26.7
CONCLUSIONS 589 ACKNOWLEDGMENT 590 REFERENCES 590 PART VII APPLICATIONS
TO CHEMICAL REACTION SYSTEMS 27 FEEDBACK-MEDIATED CONTROL OF
HYPERMEANDERING SPIRAL WAVES 593 JAN SCHLESNER, VLADIMIR ZYKOV, AND
HARALD ENGEL 27.1 INTRODUCTION 593 27.2 THE FITZHUGH-NAGUMO MODEL 594
27.3 STABILIZATION OF RIGIDLY ROTATING SPIRALS IN THE HYPERMEANDERING
REGIME 596 XVI CONTENTS 27.4 CONTROL OF SPIRAL WAVE LOCATION IN THE
HYPERMEANDERING REGIME 599 27.5 DISCUSSION 605 REFERENCES 606 28 CONTROL
OF SPATIOTEMPORAL CHAOS IN SURFACE CHEMICAL REACTIONS 609 CARSTEN BETA
AND ALEXANDER S. MIKHAILOV 28.1 INTRODUCTION 609 28.2 THE CATALYTIC CO
OXIDATION ON PT(LLO) 610 28.2.1 MECHANISM 610 28.2.2 MODELING 611 28.2.3
EXPERIMENTAL SETUP 612 28.3 SPATIOTEMPORAL CHAOS IN CATALYTIC CO
OXIDATION ON PT(LLO) 613 28.4 CONTROL OF SPATIOTEMPORAL CHAOS BY GLOBAL
DELAYED FEEDBACK 615 28.4.1 CONTROL OF TURBULENCE IN CATALYTIC CO
OXIDATION - EXPERIMENTAL 616 28.4.1.1 CONTROL OF TURBULENCE 617 28.4.1.2
SPATIOTEMPORAL PATTERN FORMATION 618 28.4.2 CONTROL OF TURBULENCE IN
CATALYTIC CO OXIDATION - NUMERICAL SIMULATIONS 619 28.4.3 CONTROL OF
TURBULENCE IN OSCILLATORY MEDIA - THEORY 621 28.4.4 TIME-DELAY
AUTOSYNCHRONIZATION 625 28.5 CONTROL OF SPATIOTEMPORAL CHAOS BY PERIODIC
FORCING 628 ACKNOWLEDGMENT 630 REFERENCES 630 29 FORCING AND FEEDBACK
CONTROL OF ARRAYS OF CHAOTIC ELECTROCHEMICAL OSCILLATORS 633 ISTUAEN Z.
KISS AND JOHN L HUDSON 29.1 INTRODUCTION 633 29.2 CONTROL OF SINGLE
CHAOTIC OSCILLATOR 634 29.2.1 EXPERIMENTAL SETUP 634 29.2.2 CHAOTIC NI
DISSOLUTION: LOW-DIMENSIONAL, PHASE COHERENT ATTRACTOR 635 29.2.2.1
UNFORCED CHAOTIC OSCILLATOR 635 29.2.2.2 PHASE OF THE UNFORCED SYSTEM
636 29.2.3 FORCING: PHASE SYNCHRONIZATION AND INTERMITTENCY 637 29.2.3.1
FORCING WITH Q=OO 0 637 29.2.3.2 FORCING WITH Q / RA 0 638 29.2.4
DELAYED FEEDBACK: TRACKING 638 29.3 CONTROL OF SMALL ASSEMBLIES OF
CHAOTIC OSCILLATORS 640 29.4 CONTROL OF OSCILLATOR POPULATIONS 642
29.4.1 GLOBAL COUPLING 642 29.4.2 PERIODIC FORCING OF ARRAYS OF CHAOTIC
OSCILLATORS 643 29.4.3 FEEDBACK ON ARRAYS OF CHAOTIC OSCILLATORS 644
29.4.4 FEEDBACK, FORCING, AND GLOBAL COUPLING: ORDER PARAMETER 645
29.4.5 CONTROL OF COMPLEXITY OF A COLLECTIVE SIGNAL 646 29.5 CONCLUDING
REMARKS 647 ACKNOWLEDGMENT 648 REFERENCES 649 PART VIII APPLICATIONS TO
BIOLOGY 30 CONTROL OF SYNCHRONIZATION IN OSCILLATORY NEURAL NETWORKS 653
PETER A. TASS, CHRISTIAN HAUPTMANN, AND OLEKSANDR V. POPOVYCH 30.1
INTRODUCTION 653 30.2 MULRISITE COORDINATED RESET STIMULATION 654 30.3
LINEAR MULTISITE DELAYED FEEDBACK 662 30.4 NONLINEAR DELAYED FEEDBACK
666 30.5 RESHAPING NEURAL NETWORKS 674 30.6 DISCUSSION 676 REFERENCES
678 31 CONTROL OF CARDIAC ELECTRICAL NONLINEAR DYNAMICS 683 TRINE
KROGH-MADSEN, PETER N. JORDAN, AND DAVIDJ. CHRISTINI 31.1 INTRODUCTION
683 31.2 CARDIAC ELECTROPHYSIOLOGY 684 31.2.1 RESTITUTION AND ALTEMANS
685 31.3 CARDIAC ARRHYTHMIAS 686 31.3.1 REENTRY 687 31.3.2 VENTRICULAR
TACHYARRHYTHMIAS 688 31.3.3 ALTEMANS AS AN ARRHYTHMIA TRIGGER 688 31.4
CURRENT TREATMENT OF ARRHYTHMIAS 689 31.4.1 PHARMACOLOGICAL TREATMENT
689 31.4.2 IMPLANTABLE CARDIOVERTER DEFIBRILLATORS 689 31.4.3 ABLATION
THERAPY 690 31.5 ALTEMANS CONTROL 691 31.5.1 CONTROLLING CELLULAR
ALTEMANS 691 31.5.2 CONTROL OF ALTEMANS IN TISSUE 692 31.5.3 LIMITATIONS
OF THE DFC ALGORITHM IN ALTEMANS CONTROL 693 31.5.4 ADAPTIVE DI CONTROL
694 31.6 CONTROL OF VENTRICULAR TACHYARRHYTHMIAS 695 31.6.1 SUPPRESSION
OF SPIRAL WAVES 696 31.6.2 ANTITACHYCARDIA PACING 696 31.6.3 UNPINNING
SPIRAL WAVES 698 31.7 CONCLUSIONS AND PROSPECTS 699 REFERENCES 700 XVIII
CONTENTS 32 CONTROLLING SPATIOTEMPORAL CHAOS AND SPIRAL TURBULENCE IN
EXCITABLE MEDIA 703 SITABHRA SINHA AND S. SRIDHAR 32.1 INTRODUCTION 703
32.2 MODELS OF SPATIOTEMPORAL CHAOS IN EXCITABLE MEDIA 706 32.3 GLOBAL
CONTROL 708 32.4 NONGLOBAL SPATIALLY EXTENDED CONTROL 711 32.4.1
APPLYING CONTROL OVER A MESH 711 32.4.2 APPLYING CONTROL OVER AN ARRAY
OF POINTS 713 32.5 LOCAL CONTROL OF SPATIOTEMPORAL CHAOS 714 32.6
DISCUSSION 716 ACKNOWLEDGMENTS 717 REFERENCES 718 PART IX APPLICATIONS
TO ENGINEERING 33 NONLINEAR CHAOS CONTROL AND SYNCHRONIZATION 721 HENRI
J. C. HUIJBERTS AND HENK NIJMEIJER 33.1 INTRODUCTION 721 33.2 NONLINEAR
GEOMETRIE CONTROL 721 33.2.1 SOME DIFFERENTIAL GEOMETRIE CONCEPTS 722
33.2.2 NONLINEAR CONTROLLABILITY 723 33.2.3 CHAOS CONTROL THROUGH
FEEDBACK LINEARIZATION 728 33.2.4 CHAOS CONTROL THROUGH INPUT-OUTPUT
LINEARIZATION 732 33.3 LYAPUNOV DESIGN 737 33.3.1 LYAPUNOV STABILITY AND
LYAPUNOVS FIRST METHOD 737 33.3.2 LYAPUNOV"S DIRECT METHOD 739 33.3.3
LASALLE'S INVARIANCE PRINCIPLE 741 33.3.4 EXAMPLES 742 REFERENCES 749 34
ELECTRONIC CHAOS CONTROLLERS - FROM THEORY TO APPLICATIONS 751 MACIEJ
OGORZAKK 34.1 INTRODUCTION 751 34.1.1 CHAOS CONTROL 752 34.1.2
FUNDAMENTAL PROPERTIES OF CHAOTIC SYSTEMS AND GOALS OFTHE CONTROL 753
34.2 REQUIREMENTS FOR ELECTRONIC IMPLEMENTATION OF CHAOS CONTROLLERS 754
34.3 SHORT DESCRIPTION OF THE OGY TECHNIQUE 755 34.4 IMPLEMENTATION
PROBLEMS FOR THE OGY METHOD 757 34.4.1 EFFECTS OF CALCULATION PRECISION
758 34.4.2 APPROXIMATE PROCEDURES FOR FINDING PERIODIC ORBITS 759 34.4.3
EFFECTS OF TIME DELAYS 759 34.5 OCCASIONAL PROPORTIONAL FEEDBACK
(HUNT"S) CONTROLLER 761 34.5.1 IMPROVED CHAOS CONTROLLER FOR AUTONOMOUS
CIRCUITS 763 34.6 EXPERIMENTAL CHAOS CONTROL SYSTEMS 765 34.6.1 CONTROL
OF A MAGNETOELASTIC RIBBON 765 34.6.2 CONTROL OF A CHAOTIC LASER 766
34.6.3 CHAOS-BASED ARRHYTHMIA SUPPRESSION AND DEFIBRILLATION 767 34.7
CONCLUSIONS 768 REFERENCES 769 35 CHAOS IN PULSE-WIDTH MODULATED CONTROL
SYSTEMS 771 ZHANYBAI T. ZHUSUBALIYEV AND ERIK MOSEKILDE 35.1
INTRODUCTION 771 35.2 DC/DC CONVERTER WITH PULSE-WIDTH MODULATED CONTROL
774 35.3 BIFURCATION ANALYSIS FOR THE DC/DC CONVERTER WITH ONE-LEVEL
CONTROL 778 35.4 DC/DC CONVERTER WITH TWO-LEVEL CONTROL 781 35.5
BIFURCATION ANALYSIS FOR THE DC/DC CONVERTER WITH TWO-LEVEL CONTROL 783
35.6 CONCLUSIONS 784 ACKNOWLEDGMENTS 788 REFERENCES 788 36 TRANSIENT
DYNAMICS OF DUFFING SYSTEM UNDER TIME-DELAYED FEEDBACK CONTROL: GLOBAL
PHASE STRUCTURE AND APPLICATION TO ENGINEERING 793 TAKASHI HIKIHARA AND
KOHEI YAMASUE 36.1 INTRODUCTION 793 36.2 TRANSIENT DYNAMICS OF TRANSIENT
BEHAVIOR 794 36.2.1 MAGNETOELASTIC BEAM AND EXPERIMENTAL SETUP 794
36.2.2 TRANSIENT BEHAVIOR 795 36.3 INITIAL FUNCTION AND DOMAIN OF
ATTRACTION 797 36.4 PERSISTENCE OF CHAOS 800 36.5 APPLICATION OF TDFC TO
NANOENGINEERING 803 36.5.1 DYNAMIC FORCE MICROSCOPY AND ITS DYNAMICS 803
36.5.2 APPLICATION OF TDFC 805 36.5.3 EXTENSION OF OPERATING RANGE 806
36.6 CONCLUSIONS 808 REFERENCES 808 SUBJECT INDEX 811 |
| adam_txt |
HANDBOOK OF CHAOS CONTROL EDITED BY ECKEHARD SCHOLL AND HEINZ GEORG
SCHUSTER 2 ND , COMPLETELY REVISED AND ENLARGED EDITION WILEY- VCH
WILEY-VCH VERLAG GMBH & CO. KGAA CONTENTS PREFACE XXI LIST OF
CONTRIBUTORS XXIII PART I BASIC ASPECTS AND EXTENSION OF METHODS 1
CONTROLLING CHAOS 3 ELBERT E. N. MACAU AND CELSO CREBOGI 1.1
INTRODUCTION 3 1.2 THE OGY CHAOS CONTROL 6 1.3 TARGETING-STEERING
CHAOTIC TRAJECTORIES 8 1.3.1 PART I: FINDING A PROPER TRAJECTORY 9 1.3.2
PART II: FINDING A PSEUDO-ORBIT TRAJECTORY 10 1.3.3 THE TARGETING
ALGORITHM 12 1.4 APPLYING CONTROL OF CHAOS AND TARGETING IDEAS 1.4.1
CONTROLLING AN ELECTRONIC CIRCUIT 13 1.4.2 CONTROLLING A COMPLEX SYSTEM
19 1.5 CONCLUSION 26 REFERENCES 26 2 TIME-DELAY CONTROL FOR DISCRETE
MAPS 29 JOSHUA E. S. SOCOLAR 2.1 OVERVIEW: WHY STUDY DISCRETE MAPS? 29
2.2 THEME AND VARIATIONS 31 2.2.1 RUDIMENTARY TIME-DELAY FEEDBACK 32
2.2.2 EXTENDING THE DOMAIN OF CONTROL 34 2.2.3 HIGH-DIMENSIONAL SYSTEMS
37 2.3 ROBUSTNESS OF TIME-DELAY STABILIZATION 41 2.4 SUMMARY 44
ACKNOWLEDGMENTS 44 REFERENCES 44 HANDBOOK OF CHAOS CONTROL, 2ND ED.
EDITED BY E. SCHOLL AND H. G. SCHUSTER COPYRIGHT 2008 WILEY-VCH VERLAG
GMBH & CO. KGAA, WEINHEIM ISBN: 978-3-527-40605-0 CONTENTS 3 AN
ANALYTICAL TREATMENT OF THE DELAYED FEEDBACK CONTROL ALGORITHM 47
KESTUTIS PYRAGAS, TATJANA PYRAGIENE, AND VIKTORAS PYRAGAS 3.1
INTRODUCTION 47 3.2 PROPORTIONAL VERSUS DELAYED FEEDBACK 50 3.3
CONTROLLING PERIODIC ORBITS ARISING FROM A PERIOD DOUBLING BIFURCATION
53 3.3.1 EXAMPLE: CONTROLLING THE ROESSLER SYSTEM 54 3.4 CONTROL OF
FORCED SELF-SUSTAINED OSCILLATIONS 57 3.4.1 PROBLEM FORMULATION AND
AVERAGED EQUATION 57 3.4.2 PERIODIC ORBITS OF THE FREE SYSTEM 58 3.4.3
LINEAR STABILITY OF THE SYSTEM CONTROUED BY DELAYED FEEDBACK 3.4.4
NUMERICAL DEMONSTRATIONS 63 3.5 CONTROLLING TORSION-FREE PERIODIC ORBITS
63 3.5.1 EXAMPLE: CONTROLLING THE LORENZ SYSTEM AT A SUBCRITICAL HOPF
BIFURCATION 65 3.6 CONCLUSIONS 68 REFERENCES 70 4 BEYOND THE ODD-NUMBER
LIMITATION OF TIME-DELAYED FEEDBACK CONTROL 73 BERNOLD FIEDLER, VALENTIN
FLUNKERT, MARC CEORGI, PHILIPP HAVEL, AND ECKEHARD SCHOLL 4.1
INTRODUCTION 73 4.2 MECHANISM OF STABILIZATION 74 4.3 CONDITIONS ON THE
FEEDBACK GAIN 78 4.4 CONCLUSION 82 ACKNOWLEDGMENTS 82 APPENDIX:
CALCULATION OF FLOQUET EXPONENTS 82 REFERENCES 83 5 ON GLOBAL PROPERTIES
OF TIME-DELAYED FEEDBACK CONTROL 85 WOLFRAM JUST 5.1 INTRODUCTION 85 5.2
A COMMENT ON CONTROL AND ROOT FINDING ALGORITHMS 88 5.3 CODIMENSION-TWO
BIFURCATIONS AND BASINS OF ATTRACTION 91 5.3.1 THE TRANSITION FROM
SUPER- TO SUBCRITICAL BEHAVIOR 91 5.3.2 PROBING BASINS OF ATTRACTION IN
EXPERIMENTS 93 5.4 A CASE STUDY OF GLOBAL FEATURES FOR TIME-DELAYED
FEEDBACK CONTROL 94 5.4.1 ANALYTICAL BIFURCATION ANALYSIS OF
ONE-DIMENSIONAL MAPS 95 5.4.2 DEPENDENCE OF SUB- AND SUPERCRITICAL
BEHAVIOR ON THE OBSERVABLE 98 5.4.3 INFLUENCE OF THE COUPLING OF THE
CONTROL FORCE 99 5.5 CONCLUSION 101 CONTENTS VII ACKNOWLEDGMENTS , 102
APPENDIX A. NORMAL FORM REDUCTION 103 APPENDIX B. SUPER- AND SUBCRITICAL
HOPF BIFURCATION FOR MAPS 106 REFERENCES 106 6 POINCARE-BASED CONTROL OF
DELAYED MEASURED SYSTEMS: LIMITATIONS AND IMPROVED CONTROL 109 JENS
CHRISTIAN CLAUSSEN 6.1 INTRODUCTION 109 6.1.1 THE DELAY
PROBLEM-TIME-DISCRETE CASE 109 6.1.2 EXPERIMENTAL SETUPS WITH DELAY 111
6.2 OTT-GREBOGI-YORKE (OGY) CONTROL 112 6.3 LIMITATIONS OF UNMODIFIED
CONTROL AND SIMPLE IMPROVED CONTROL SCHEINES 113 6.3.1 LIMITATIONS OF
UNMODIFIED OGY CONTROL IN THE PRESENCE OF DELAY 113 6.3.2 STABILITY
DIAGRAMS DERIVED BY THE JURY CRITERION 116 6.3.3 STABILIZING UNKNOWN
FIXED POINTS: LIMITATIONS OF UNMODIFIED DIFFERENCE CONTROL 116 6.3.4
RHYTHMIC CONTROL SCHEMES: RHYTHMIC OGY CONTROL 119 6.3.5 RHYTHMIC
DIFFERENCE CONTROL 120 6.3.6 A SIMPLE MEMORY CONTROL SCHEME: USING STATE
SPACE MEMORY 122 6.4 OPTIMAL IMPROVED CONTROL SCHEMES 123 6.4.1 LINEAR
PREDICTIVE LOGGING CONTROL (LPLC) 123 6.4.2 NONLINEAR PREDICTIVE LOGGING
CONTROL 124 6.4.3 STABILIZATION OF UNKNOWN FIXED POINTS: MEMORY
DIFFERENCE CONTROL (MDC) 125 6.5 SUMMARY 126 REFERENCES 127 7 NONLINEAR
AND ADAPTIVE CONTROL OF CHAOS 129 ALEXANDER FRADKOV AND ALEXANDER
POGROMSKY 7.1 INTRODUCTION 129 7.2 CHAOS AND CONTROL: PRELIMINARIES 130
7.2.1 DEFINITIONS OF CHAOS 130 7.2.2 MODELS OF CONTROLLED SYSTEMS 131
7.2.3 CONTROL GOALS 132 7.3 METHODS OF NONLINEAR CONTROL 134 7.3.1
GRADIENT METHOD 135 7.3.2 SPEED-GRADIENT METHOD 136 7.3.3 FEEDBACK
LINEARIZATION 141 7.3.4 OTHER METHODS 142 7.3.5 GRADIENT CONTROL OF THE
HENON SYSTEM 144 7.3.6 FEEDBACK LINEARIZATION CONTROL OF THE LORENZ
SYSTEM 146 VIII CONTENTS 7.3.7 SPEED-GRADIENT STABILIZATION OF THE
EQUILIBRIUM POINT FOR THE THERMAL CONVECTION LOOP MODEL 147 7.4 ADAPTIVE
CONTROL 148 7.4.1 GENERAL DEFINITIONS 148 7.4.2 ADAPTIVE MASTER-SLAVE
SYNCHRONIZATION OF ROESSLER SYSTEMS 149 7.5 OTHER PROBLEMS 154 7.6
CONCLUSIONS 155 ACKNOWLEDGMENT 155 REFERENCES 156 PART II CONTROLLING
SPACE-TIME CHAOS 8 LOCALIZED CONTROL OF SPATIOTEMPORAL CHAOS 161 ROMAN
O. CRIGORIEV AND ANDREAS HANDEL 8.1 INTRODUCTION 161 8.1.1 EMPIRICAL
CONTROL 163 8.1.2 MODEL-BASED CONTROL 164 8.2 SYMMETRY AND THE MINIMAL
NUMBER OF SENSORS/ACTUATORS 167 8.3 NONNORMALITY AND NOISE AMPLIFICATION
170 8.4 NONLINEARITY AND THE CRITICAL NOISE LEVEL 175 8.5 CONCLUSIONS
177 REFERENCES 177 9 CONTROLLING SPATIOTEMPORAL CHAOS: THE PARADIGM OF
THE COMPLEX GINZBURG-LANDAU EQUATION 181 STEFANO BOCCALETTI AND JEAN
BRAGARD 9.1 INTRODUCTION 181 9.2 THE COMPLEX GINZBURG-LANDAU EQUATION
183 9.2.1 DYNAMICS CHARACTERIZATION 185 9.3 CONTROL OF THE CGLE 187 9.4
CONCLUSIONS AND PERSPECTIVES 192 ACKNOWLEDGMENT 193 REFERENCES 193 10
MULTIPLE DELAY FEEDBACK CONTROL 197 ALEXANDER AHLBORN AND ULRICH PARLITZ
10.1 INTRODUCTION 197 10.2 MULTIPLE DELAY FEEDBACK CONTROL 198 10.2.1
LINEAR STABILITY ANALYSIS 199 10.2.2 EXAMPLE: COLPITTS OSCILLATOR 200
10.2.3 COMPARISON WITH HIGH-PASS FILTER AND PD CONTROLLER 203 10.2.4
TRANSFER FUNCTION OFMDFC 204 10.3 FROM MULTIPLE DELAY FEEDBACK CONTROL
TO NOTCH FILTER FEEDBACK 206 10.4 CONTROLLABILITY CRITERIA 208 10.4.1
MULTIPLE DELAY FEEDBACK CONTROL 209 10.4.2 NOTCH FILTER FEEDBACK AND
HIGH-PASS FILTER 210 10.5 LASER STABILIZATION USING MDFC AND NFF 211
10.6 CONTROLLING SPATIOTEMPORAL CHAOS 213 10.6.1 THE GINZBURG-LANDAU
EQUATION 213 10.6.2 CONTROLLING TRAVELING PLANE WAVES 214 10.6.3 LOCAL
FEEDBACK CONTROL 215 10.7 CONCLUSION 218 REFERENCES 219 PART III
CONTROLLING NOISY MOTION 11 CONTROL OF NOISE-INDUCED DYNAMICS 223
NATALIA B. JANSON, ALEXANDER C. BALANOV, AND ECKEHARD SCHOLL 11.1
INTRODUCTION 223 11.2 NOISE-INDUCED OSCILLATIONS BELOW ANDRONOV-HOPF
BIFURCATION AND THEIR CONTROL 226 11.2.1 WEAK NOISE AND CONTROL:
CORRELATION FUNCTION 228 11.2.2 WEAK NOISE AND NO CONTROL: CORRELATION
TIME AND SPECTRUM 229 11.2.3 WEAK NOISE AND CONTROL: CORRELATION TIME
231 11. 2 .4 WEAK NOISE AND CONTROL: SPECTRUM 235 11.2.5 ANY NOISE AND
NO CONTROL: CORRELATION TIME 236 11.2.6 ANY NOISE AND CONTROL:
CORRELATION TIME AND SPECTRUM 238 11.2.7 SO, WHAT CAN WE CONTROL? 240
11.3 NOISE-INDUCED OSCILLATIONS IN AN EXCITABLE SYSTEM AND THEIR CONTROL
241 11.3.1 COHERENCE RESONANCE IN THE FITZHUGH-NAGUMO SYSTEM 243 11.3.2
CORRELATION TIME AND SPECTRUM WHEN FEEDBACK IS APPLIED 244 11.3.3
CONTROL OF SYNCHRONIZATION IN COUPLED FITZHUGH-NAGUMO SYSTEMS 245 11.3.4
WHAT CAN WE CONTROL IN AN EXCITABLE SYSTEM? 246 11.4 DELAYED FEEDBACK
CONTROL OF NOISE-INDUCED PULSES IN A MODEL OF AN EXCITABLE MEDIUM 247
11.4.1 MODEL DESCRIPTION 247 11.4.2 CHARACTERISTICS OF NOISE-INDUCED
PATTERNS 249 11.4.3 CONTROL OF NOISE-INDUCED PATTERNS 251 11.4.4
MECHANISMS OF DELAYED FEEDBACK CONTROL OF THE EXCITABLE MEDIUM 253
11.4.5 WHAT CAN BE CONTROLLED IN AN EXCITABLE MEDIUM? 254 11.5 DELAYED
FEEDBACK CONTROL OF NOISE-INDUCED PATTERNS IN A GLOBALLY COUPLED
REACTION-DIFFUSION MODEL 255 11.5.1 SPATIOTEMPORAL DYNAMICS IN THE
UNCONTROLLED DETERMINISTIC SYSTEM 256 11.5.2 NOISE-INDUCED PATTERNS IN
THE UNCONTROLLED SYSTEM 258 11.5.3 TIME-DELAYED FEEDBACK CONTROL OF
NOISE-INDUCED PATTERNS 260 11.5.4 LINEAR MODES OF THE INHOMOGENEOUS
FIXED POINT 264 11.5.5 DELAY-INDUCED OSCILLATORY PATTERNS 268 11.5.6
WHAT CAN BE CONTROUED IN A GLOBALLY COUPLED REACTION-DIFFUSION SYSTEM?
269 11.6 SUMMARY AND CONCLUSIONS 270 ACKNOWLEDGMENTS 270 REFERENCES 270
12 CONTROLLING COHERENCE OF NOISY AND CHAOTIC OSCILLATORS BY DELAYED
FEEDBACK 275 DENIS COLDOBIN, MICHAEL ROSENBLUM, AND ARKADY PIKOVSKY 12.1
CONTROL OF COHERENCE: NUMERICAL RESULTS 276 12.1.1 NOISY OSCILLATOR 276
12.1.2 CHAOTIC OSCILLATOR 277 12.1.3 ENHANCING PHASE SYNCHRONIZATION 279
12.2 THEORY OF COHERENCE CONTROL 279 12.2.1 BASIC PHASE MODEL 279 12.2.2
NOISE-FREE CASE 280 12.2.3 GAUSSIAN APPROXIMATION 280 12.2.4
SELF-CONSISTENT EQUATION FOR DIFFUSION CONSTANT 282 12.2.5 COMPARISON OF
THEORY AND NUMERICS 283 12.3 CONTROL OF COHERENCE BY MULTIPLE DELAYED
FEEDBACK 283 12.4 CONCLUSION 288 REFERENCES 289 13 RESONANCES INDUCED BY
THE DELAY TIME IN NONLINEAR AUTONOMOUS OSCILLATORS WITH FEEDBACK 291
CRISTINA MASOLLER ACKNOWLEDGMENT 298 REFERENCES 299 PART IV
COMMUNICATING WITH CHAOS, CHAOS SYNCHRONIZATION 14 SECURE COMMUNICATION
WITH CHAOS SYNCHRONIZATION 303 WOLFGANG KINZEL AND IDO KANTER 14.1
INTRODUCTION 303 14.2 SYNCHRONIZATION OF CHAOTIC SYSTEMS 304 14.3 CODING
AND DECODING SECRET MESSAGES IN CHAOTIC SIGNALS 309 14 .4 ANALYSIS OF
THE EXCHANGED SIGNAL 311 14.5 NEURAL CRYPTOGRAPHY 313 14.6 PUBLIC KEY
EXCHANGE BY MUTUAL SYNCHRONIZATION 315 14.7 PUBLIC KEYS BY ASYMMETRIE
ATTRACTORS 318 14.8 MUTUAL CHAOS PASS FILTER 319 14.9 DISCUSSION 321
REFERENCES 323 15 NOISE ROBUST CHAOTIC SYSTEMS 325 THOMAS L CARROLL 15.1
INTRODUCTION 325 15.2 CHAOTIC SYNCHRONIZATION 326 15.3 2-FREQUENCY
SELF-SYNCHRONIZING CHAOTIC SYSTEMS 326 15.3.1 SIMPLE MAPS 326 15.4
2-FREQUENCY SYNCHRONIZATION IN FLOWS 329 15.4.1 2-FREQUENCY ADDITIVE
ROESSLER 329 15.4.2 PARAMETER VARIATION AND PERIODIC ORBITS 332 15.4.3
UNSTABLE PERIODIC ORBITS 333 15.4.4 FLOQUET MULTIPLIERS 334 15.4.5
LINEWIDTHS 335 15.5 CIRCUIT EXPERIMENTS 336 15.5.1 NOISE EFFECTS 338
15.6 COMMUNICATION SIMULATIONS 338 15.7 MULTIPLICATIVE TWO-FREQUENCY
ROESSLER CIRCUIT 341 15.8 CONCLUSIONS 346 REFERENCES 346 16 NONLINEAR
COMMUNICATION STRATEGIES 349 HENRY D. I. ABARBANEL 16.1 INTRODUCTION 349
16.1.1 SECRECY, ENCRYPTION, AND SECURITY? 350 16.2 SYNCHRONIZATION 351
16.3 COMMUNICATING USING CHAOTIC CARRIERS 353 16.4 TWO EXAMPLES FROM
OPTICAL COMMUNICATION 355 16.4.1 RARE-EARTH-DOPED FIBER AMPLIFIER LASER
355 16.4.2 TIME DELAY OPTOELECTRONIC FEEDBACK SEMICONDUCTOR LASER 357
16.5 CHAOTIC PULSE POSITION COMMUNICATION 359 16.6 WHY USE CHAOTIC
SIGNALS AT ALL? 362 16.7 UNDISTORTING THE NONLINEAR EFFECTS OF THE
COMMUNICATION CHANNEL 363 16.8 CONCLUSIONS 366 REFERENCES 367 17
SYNCHRONIZATION AND MESSAGE TRANSMISSION FOR NETWORKED CHAOTIC OPTICAL
COMMUNICATIONS 369 K. ALAN SHORE, PAUL S. SPENCER, AND LLESTYN PIERCE
17.1 INTRODUCTION 369 17.2 SYNCHRONIZATION AND MESSAGE TRANSMISSION 370
17.3 NETWORKED CHAOTIC OPTICAL COMMUNICATION 372 17.3.1 CHAOS
MULTIPLEXING 373 17.3.2 MESSAGE RELAY 373 17.3.3 MESSAGE BROADCASTING
374 XII CONTENTS 17.4 SUMMARY 376 ACKNOWLEDGMENTS 376 REFERENCES 376 18
FEEDBACK CONTROL PRINCIPLES FOR PHASE SYNCHRONIZATION 379 VLADIMIR N.
BELYKH, CRIGORY V. OSIPOV, AND JUERGEN KURTHS 18.1 INTRODUCTION 379 18.2
GENERAL PRINCIPLES OF AUTOMATIC SYNCHRONIZATION 381 18.3 TWO COUPLED
POINCARE SYSTEMS 384 18.4 COUPLED VAN DER POL AND ROESSLER OSCILLATORS
386 18.5 TWO COUPLED ROESSLER OSCILLATORS 389 18.6 COUPLED ROESSLER AND
LORENZ OSCILLATORS 391 18.7 PRINCIPLES OF AUTOMATIC SYNCHRONIZATION IN
NETWORKS OF COUPLED OSCILLATORS 393 18.8 SYNCHRONIZATION OF LOCALLY
COUPLED REGULAER OSCILLATORS 395 18.9 SYNCHRONIZATION OF LOCALLY COUPLED
CHAOTIC OSCILLATORS 397 18.10 SYNCHRONIZATION OF GLOBALLY COUPLED
CHAOTIC OSCILLATORS 399 18.11 CONCLUSIONS 401 REFERENCES 401 PART V
APPLICATIONS TO OPTICS 19 CONTROLLING FAST CHAOS IN OPTOELECTRONIC DELAY
DYNAMICAL SYSTEMS 407 LUCAS LLLING, DANIEL J. CAUTHIER, AND JONATHAN N.
BLAKELY 19.1 INTRODUCTION 407 19.2 CONTROL-LOOP LATENCY: A SIMPLE
EXAMPLE 408 19.3 CONTROLLING FAST SYSTEMS 412 19.4 A FAST OPTOELECTRONIC
CHAOS GENERATOR 415 19.5 CONTROLLING THE FAST OPTOELECTRONIC DEVICE 419
19.6 OUTLOOK 423 ACKNOWLEDGMENT 424 REFERENCES 424 20 CONTROL OF
BROAD-AREA LASER DYNAMICS WITH DELAYED OPTICAL FEEDBACK 427 NICOLETA
CACIU, EDELTRAUD GEHRIG, AND ORTWIN HESS 20.1 INTRODUCTION:
SPATIOTEMPORALLY CHAOTIC SEMICONDUCTOR LASERS 427 20.2 THEORY: TWO-LEVEL
MAXWELL-BLOCH EQUATIONS 429 20.3 DYNAMICS OF THE SOLITARY LASER 432 20.4
DETECTION OF SPATIOTEMPORAL COMPLEXITY 433 20.4.1 REDUCTION OF THE
NUMBER OF MODES BY COHERENT INJECTION 433 20.4.2 PULSE-INDUCED MODE
SYNCHRONIZATION 435 20.5 SELF-INDUCED STABILIZATION AND CONTROL WITH
DELAYED OPTICAL FEEDBACK 438 CONTENTS XII I 20.5.1 INFLUENCE OF DELAYED
OPTICAL FEEDBACK 439 20.5.2 INFLUENCE OF THE DELAY TIME 440 20.5.3
SPATIALLY STRUCTURED DELAYED OPTICAL FEEDBACK CONTROL 444 20.5.4
FILTERED SPATIALLY STRUCTURED DELAYED OPTICAL FEEDBACK 449 20.6
CONCLUSIONS 451 REFERENCES 453 21 NONINVASIVE CONTROL OF SEMICONDUCTOR
LASERS BY DELAYED OPTICAL FEEDBACK 455 HANS-JUERGEN WUENSCHE, SYLVIA
SCHIKORA, AND FRITZ HENNEBERGER 21.1 THE ROLE OF THE OPTICAL PHASE 456
21.2 GENERIC LINEAR MODEL 459 21.3 GENERALIZED LANG-KOBAYASHI MODEL 461
21.4 EXPERIMENT 462 21.4.1 THE INTEGRATED TANDEM LASER 463 21.4.2 DESIGN
OF THE CONTROL CAVITY 464 21.4.3 MAINTAINING RESONANCE 465 21.4.4
LATENCY AND COUPLING STRENGTH 465 21.4.5 RESULTS OF THE CONTROL
EXPERIMENT 466 21.5 NUMERICAL SIMULATION 468 21.5.1 TRAVELING-WAVE MODEL
468 21.5.2 NONINVASIVE CONTROL BEYOND A HOPF BIFURCATION 470 21.5.3
CONTROL DYNAMICS 470 21.5.4 VARIATION OF THE CONTROL PARAMETERS 471 21.6
CONCLUSIONS 473 ACKNOWLEDGMENT 473 REFERENCES 473 22 CHAOS AND CONTROL
IN SEMICONDUCTOR LASERS 475 JUNJI OHTSUBO 22.1 INTRODUCTION 475 22.2
CHAOS IN SEMICONDUCTOR LASERS 476 22.2.1 LASER CHAOS 476 22.2.2 OPTICAL
FEEDBACK EFFECTS IN SEMICONDUCTOR LASERS 478 22.2.3 CHAOTIC EFFECTS IN
NEWLY DEVELOPED SEMICONDUCTOR LASERS 480 22.3 CHAOS CONTROL IN
SEMICONDUCTOR LASERS 485 22.4 CONTROL IN NEWLY DEVELOPED SEMICONDUCTOR
LASERS 494 22.5 CONCLUSIONS 497 REFERENCES 498 XIV CONTENTS 23 FROM
PATTERN CONTROL TO SYNCHRONIZATION: CONTROL TECHNIQUES IN NONLINEAR
OPTICAL FEEDBACK SYSTEMS 501 BJOERN GUETLICH AND CORNELIA DENZ 23.1
CONTROL METHODS FOR SPATIOTEMPORAL SYSTEMS 502 23.2 OPTICAL
SINGLE-FEEDBACK SYSTEMS 503 23.2.1 A SIMPLIFIED SINGLE-FEEDBACK MODEL
SYSTEM 504 23.2.2 THE PHOTOREFRACTIVE SINGLE-FEEDBACK SYSTEM - COHERENT
NONLINEARITY 506 23.2.3 THEORETICAL DESCRIPTION OF THE PHOTOREFRACTIVE
SINGLE-FEEDBACK SYSTEM 508 23.2.4 LINEAR STABILITY ANALYSIS 509 23.2.5
THE LCLV SINGLE-FEEDBACK SYSTEM - INCOHERENT NONLINEARITY 510 23.2.6
PHASE-ONLY MODE 511 23.2.7 POLARIZATION MODE 513 23.2.8 DISSIPATIVE
SOLITONS IN THE LCLV FEEDBACK SYSTEM 513 23.3 SPATIAL FOURIER CONTROL
514 23.3.1 EXPERIMENTAL DETERMINATION OF MARGINAL INSTABILITY 516 23.3.2
STABILIZATION OF UNSTABLE PATTERN 517 23.3.3 DIRECT FOURIER FILTERING
518 23.3.4 POSITIVE FOURIER CONTROL 518 23.3.5 NONINVASIVE FOURIER
CONTROL 519 23.4 REAL-SPACE CONTROL 520 23.4.1 INVASIVE FORCING 520
23.4.2 POSITIONING OF LOCALIZED STATES 522 23.4.3 SYSTEM HOMOGENIZATION
522 23.4.4 STATIC POSITIONING 523 23.4.5 ADDRESSING AND DYNAMIC
POSITIONING 523 23.5 SPATIOTEMPORAL SYNCHRONIZATION 524 23.5.1 SPATIAL
SYNCHRONIZATION OF PERIODIC PATTERN 524 23.5.2 UNIDIRECTIONAL
SYNCHRONIZATION OF TWO LCLV SYSTEMS 525 23.5.3 SYNCHRONIZATION OF
SPATIOTEMPORAL COMPLEXITY 526 23.6 CONCLUSIONS AND OUTLOOK 527
REFERENCES 528 PART VI APPLICATIONS TO ELECTRONIC SYSTEMS 24
DELAYED-FEEDBACK CONTROL OF CHAOTIC SPATIOTEMPORAL PATTERNS IN
SEMICONDUCTOR NANOSTRUCTURES 533 ECKEHARD SCHOLL 24.1 INTRODUCTION 533
24.2 CONTROL OF CHAOTIC DOMAIN AND FRONT PATTERNS IN SUPERLATTICES 536
24.3 CONTROL OF CHAOTIC SPATIOTEMPORAL OSCILLATIONS IN RESONANT
TUNNELING DIODES 544 24.4 CONCLUSIONS 553 ACKNOWLEDGMENTS 554 REFERENCES
554 25 OBSERVING GLOBAL PROPERTIES OF TIME-DELAYED FEEDBACK CONTROL IN
ELECTRONIC CIRCUITS 559 HARTMUT BENINER, CHOL-UNG CHOE, KLAUS HOEHNE,
CLEMENS VON LOEWENICH, HIROYUKI SHIRAHAMA, AND WOLFRAM JUST 25.1
INTRODUCTION 559 25.2 DISCONTINUOUS TRANSITIONS FOR EXTENDED
TIME-DELAYED FEEDBACK CONTROL 560 25.2.1 THEORETICAL CONSIDERATIONS 560
25.2.2 EXPERIMENTAL SETUP 561 25.2.3 OBSERVATION OF BISTABILITY 562
25.2.4 BASIN OF ATTRACTION 564 25.3 CONTROLLING TORSION-FREE UNSTABLE
ORBITS 565 25.3.1 APPLYING THE CONCEPT OF AN UNSTABLE CONTROLLER 567
25.3.2 EXPERIMENTAL DESIGN OF AN UNSTABLE VAN DER POL OSCILLATOR 567
25.3.3 CONTROL COUPLING AND BASIN OF ATTRACTION 569 25.4 CONCLUSIONS 572
REFERENCES 573 26 APPLICATION OF A BLACK BOX STRATEGY TO CONTROL CHAOS
575 ACHIM KITTEL AND MARTIN POPP 26.1 INTRODUCTION 575 26.2 THE MODEL
SYSTEMS 575 26.2.1 SHINRIKI OSCILLATOR 576 26.2.2 MACKEY-GLASS TYPE
OSCILLATOR 577 26.3 THE CONTROLLER 580 26.4 RESULTS OF THE APPLICATION
OF THE CONTROLLER TO THE SHINRIKI OSCILLATOR 582 26.4.1 SPECTROSCOPY OF
UNSTABLE PERIODIC ORBITS 584 26.5 RESULTS OF THE APPLICATION OF THE
CONTROLLER TO THE MACKEY-GLASS OSCILLATOR 585 26.5.1 SPECTROSCOPY OF
UNSTABLE PERIODIC ORBITS 587 26.6 FURTHER IMPROVEMENTS 589 26.7
CONCLUSIONS 589 ACKNOWLEDGMENT 590 REFERENCES 590 PART VII APPLICATIONS
TO CHEMICAL REACTION SYSTEMS 27 FEEDBACK-MEDIATED CONTROL OF
HYPERMEANDERING SPIRAL WAVES 593 JAN SCHLESNER, VLADIMIR ZYKOV, AND
HARALD ENGEL 27.1 INTRODUCTION 593 27.2 THE FITZHUGH-NAGUMO MODEL 594
27.3 STABILIZATION OF RIGIDLY ROTATING SPIRALS IN THE HYPERMEANDERING
REGIME 596 XVI CONTENTS 27.4 CONTROL OF SPIRAL WAVE LOCATION IN THE
HYPERMEANDERING REGIME 599 27.5 DISCUSSION 605 REFERENCES 606 28 CONTROL
OF SPATIOTEMPORAL CHAOS IN SURFACE CHEMICAL REACTIONS 609 CARSTEN BETA
AND ALEXANDER S. MIKHAILOV 28.1 INTRODUCTION 609 28.2 THE CATALYTIC CO
OXIDATION ON PT(LLO) 610 28.2.1 MECHANISM 610 28.2.2 MODELING 611 28.2.3
EXPERIMENTAL SETUP 612 28.3 SPATIOTEMPORAL CHAOS IN CATALYTIC CO
OXIDATION ON PT(LLO) 613 28.4 CONTROL OF SPATIOTEMPORAL CHAOS BY GLOBAL
DELAYED FEEDBACK 615 28.4.1 CONTROL OF TURBULENCE IN CATALYTIC CO
OXIDATION - EXPERIMENTAL 616 28.4.1.1 CONTROL OF TURBULENCE 617 28.4.1.2
SPATIOTEMPORAL PATTERN FORMATION 618 28.4.2 CONTROL OF TURBULENCE IN
CATALYTIC CO OXIDATION - NUMERICAL SIMULATIONS 619 28.4.3 CONTROL OF
TURBULENCE IN OSCILLATORY MEDIA - THEORY 621 28.4.4 TIME-DELAY
AUTOSYNCHRONIZATION 625 28.5 CONTROL OF SPATIOTEMPORAL CHAOS BY PERIODIC
FORCING 628 ACKNOWLEDGMENT 630 REFERENCES 630 29 FORCING AND FEEDBACK
CONTROL OF ARRAYS OF CHAOTIC ELECTROCHEMICAL OSCILLATORS 633 ISTUAEN Z.
KISS AND JOHN L HUDSON 29.1 INTRODUCTION 633 29.2 CONTROL OF SINGLE
CHAOTIC OSCILLATOR 634 29.2.1 EXPERIMENTAL SETUP 634 29.2.2 CHAOTIC NI
DISSOLUTION: LOW-DIMENSIONAL, PHASE COHERENT ATTRACTOR 635 29.2.2.1
UNFORCED CHAOTIC OSCILLATOR 635 29.2.2.2 PHASE OF THE UNFORCED SYSTEM
636 29.2.3 FORCING: PHASE SYNCHRONIZATION AND INTERMITTENCY 637 29.2.3.1
FORCING WITH Q=OO 0 637 29.2.3.2 FORCING WITH Q / RA 0 638 29.2.4
DELAYED FEEDBACK: TRACKING 638 29.3 CONTROL OF SMALL ASSEMBLIES OF
CHAOTIC OSCILLATORS 640 29.4 CONTROL OF OSCILLATOR POPULATIONS 642
29.4.1 GLOBAL COUPLING 642 29.4.2 PERIODIC FORCING OF ARRAYS OF CHAOTIC
OSCILLATORS 643 29.4.3 FEEDBACK ON ARRAYS OF CHAOTIC OSCILLATORS 644
29.4.4 FEEDBACK, FORCING, AND GLOBAL COUPLING: ORDER PARAMETER 645
29.4.5 CONTROL OF COMPLEXITY OF A COLLECTIVE SIGNAL 646 29.5 CONCLUDING
REMARKS 647 ACKNOWLEDGMENT 648 REFERENCES 649 PART VIII APPLICATIONS TO
BIOLOGY 30 CONTROL OF SYNCHRONIZATION IN OSCILLATORY NEURAL NETWORKS 653
PETER A. TASS, CHRISTIAN HAUPTMANN, AND OLEKSANDR V. POPOVYCH 30.1
INTRODUCTION 653 30.2 MULRISITE COORDINATED RESET STIMULATION 654 30.3
LINEAR MULTISITE DELAYED FEEDBACK 662 30.4 NONLINEAR DELAYED FEEDBACK
666 30.5 RESHAPING NEURAL NETWORKS 674 30.6 DISCUSSION 676 REFERENCES
678 31 CONTROL OF CARDIAC ELECTRICAL NONLINEAR DYNAMICS 683 TRINE
KROGH-MADSEN, PETER N. JORDAN, AND DAVIDJ. CHRISTINI 31.1 INTRODUCTION
683 31.2 CARDIAC ELECTROPHYSIOLOGY 684 31.2.1 RESTITUTION AND ALTEMANS
685 31.3 CARDIAC ARRHYTHMIAS 686 31.3.1 REENTRY 687 31.3.2 VENTRICULAR
TACHYARRHYTHMIAS 688 31.3.3 ALTEMANS AS AN ARRHYTHMIA TRIGGER 688 31.4
CURRENT TREATMENT OF ARRHYTHMIAS 689 31.4.1 PHARMACOLOGICAL TREATMENT
689 31.4.2 IMPLANTABLE CARDIOVERTER DEFIBRILLATORS 689 31.4.3 ABLATION
THERAPY 690 31.5 ALTEMANS CONTROL 691 31.5.1 CONTROLLING CELLULAR
ALTEMANS 691 31.5.2 CONTROL OF ALTEMANS IN TISSUE 692 31.5.3 LIMITATIONS
OF THE DFC ALGORITHM IN ALTEMANS CONTROL 693 31.5.4 ADAPTIVE DI CONTROL
694 31.6 CONTROL OF VENTRICULAR TACHYARRHYTHMIAS 695 31.6.1 SUPPRESSION
OF SPIRAL WAVES 696 31.6.2 ANTITACHYCARDIA PACING 696 31.6.3 UNPINNING
SPIRAL WAVES 698 31.7 CONCLUSIONS AND PROSPECTS 699 REFERENCES 700 XVIII
CONTENTS 32 CONTROLLING SPATIOTEMPORAL CHAOS AND SPIRAL TURBULENCE IN
EXCITABLE MEDIA 703 SITABHRA SINHA AND S. SRIDHAR 32.1 INTRODUCTION 703
32.2 MODELS OF SPATIOTEMPORAL CHAOS IN EXCITABLE MEDIA 706 32.3 GLOBAL
CONTROL 708 32.4 NONGLOBAL SPATIALLY EXTENDED CONTROL 711 32.4.1
APPLYING CONTROL OVER A MESH 711 32.4.2 APPLYING CONTROL OVER AN ARRAY
OF POINTS 713 32.5 LOCAL CONTROL OF SPATIOTEMPORAL CHAOS 714 32.6
DISCUSSION 716 ACKNOWLEDGMENTS 717 REFERENCES 718 PART IX APPLICATIONS
TO ENGINEERING 33 NONLINEAR CHAOS CONTROL AND SYNCHRONIZATION 721 HENRI
J. C. HUIJBERTS AND HENK NIJMEIJER 33.1 INTRODUCTION 721 33.2 NONLINEAR
GEOMETRIE CONTROL 721 33.2.1 SOME DIFFERENTIAL GEOMETRIE CONCEPTS 722
33.2.2 NONLINEAR CONTROLLABILITY 723 33.2.3 CHAOS CONTROL THROUGH
FEEDBACK LINEARIZATION 728 33.2.4 CHAOS CONTROL THROUGH INPUT-OUTPUT
LINEARIZATION 732 33.3 LYAPUNOV DESIGN 737 33.3.1 LYAPUNOV STABILITY AND
LYAPUNOVS FIRST METHOD 737 33.3.2 LYAPUNOV"S DIRECT METHOD 739 33.3.3
LASALLE'S INVARIANCE PRINCIPLE 741 33.3.4 EXAMPLES 742 REFERENCES 749 34
ELECTRONIC CHAOS CONTROLLERS - FROM THEORY TO APPLICATIONS 751 MACIEJ
OGORZAKK 34.1 INTRODUCTION 751 34.1.1 CHAOS CONTROL 752 34.1.2
FUNDAMENTAL PROPERTIES OF CHAOTIC SYSTEMS AND GOALS OFTHE CONTROL 753
34.2 REQUIREMENTS FOR ELECTRONIC IMPLEMENTATION OF CHAOS CONTROLLERS 754
34.3 SHORT DESCRIPTION OF THE OGY TECHNIQUE 755 34.4 IMPLEMENTATION
PROBLEMS FOR THE OGY METHOD 757 34.4.1 EFFECTS OF CALCULATION PRECISION
758 34.4.2 APPROXIMATE PROCEDURES FOR FINDING PERIODIC ORBITS 759 34.4.3
EFFECTS OF TIME DELAYS 759 34.5 OCCASIONAL PROPORTIONAL FEEDBACK
(HUNT"S) CONTROLLER 761 34.5.1 IMPROVED CHAOS CONTROLLER FOR AUTONOMOUS
CIRCUITS 763 34.6 EXPERIMENTAL CHAOS CONTROL SYSTEMS 765 34.6.1 CONTROL
OF A MAGNETOELASTIC RIBBON 765 34.6.2 CONTROL OF A CHAOTIC LASER 766
34.6.3 CHAOS-BASED ARRHYTHMIA SUPPRESSION AND DEFIBRILLATION 767 34.7
CONCLUSIONS 768 REFERENCES 769 35 CHAOS IN PULSE-WIDTH MODULATED CONTROL
SYSTEMS 771 ZHANYBAI T. ZHUSUBALIYEV AND ERIK MOSEKILDE 35.1
INTRODUCTION 771 35.2 DC/DC CONVERTER WITH PULSE-WIDTH MODULATED CONTROL
774 35.3 BIFURCATION ANALYSIS FOR THE DC/DC CONVERTER WITH ONE-LEVEL
CONTROL 778 35.4 DC/DC CONVERTER WITH TWO-LEVEL CONTROL 781 35.5
BIFURCATION ANALYSIS FOR THE DC/DC CONVERTER WITH TWO-LEVEL CONTROL 783
35.6 CONCLUSIONS 784 ACKNOWLEDGMENTS 788 REFERENCES 788 36 TRANSIENT
DYNAMICS OF DUFFING SYSTEM UNDER TIME-DELAYED FEEDBACK CONTROL: GLOBAL
PHASE STRUCTURE AND APPLICATION TO ENGINEERING 793 TAKASHI HIKIHARA AND
KOHEI YAMASUE 36.1 INTRODUCTION 793 36.2 TRANSIENT DYNAMICS OF TRANSIENT
BEHAVIOR 794 36.2.1 MAGNETOELASTIC BEAM AND EXPERIMENTAL SETUP 794
36.2.2 TRANSIENT BEHAVIOR 795 36.3 INITIAL FUNCTION AND DOMAIN OF
ATTRACTION 797 36.4 PERSISTENCE OF CHAOS 800 36.5 APPLICATION OF TDFC TO
NANOENGINEERING 803 36.5.1 DYNAMIC FORCE MICROSCOPY AND ITS DYNAMICS 803
36.5.2 APPLICATION OF TDFC 805 36.5.3 EXTENSION OF OPERATING RANGE 806
36.6 CONCLUSIONS 808 REFERENCES 808 SUBJECT INDEX 811 |
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| any_adam_object_boolean | 1 |
| author2 | Schöll, Eckehard 1951- |
| author2_role | edt |
| author2_variant | e s es |
| author_GND | (DE-588)11019019X |
| author_facet | Schöll, Eckehard 1951- |
| building | Verbundindex |
| bvnumber | BV022487433 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.35 |
| callnumber-search | QA402.35 |
| callnumber-sort | QA 3402.35 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 230 SK 845 SK 880 UF 1950 UG 3900 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)181925505 (DE-599)DNB983933677 |
| dewey-full | 003/.857 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.857 |
| dewey-search | 003/.857 |
| dewey-sort | 13 3857 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Physik Informatik Mathematik Wirtschaftswissenschaften |
| edition | 2., completely rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV022487433 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:50:34Z |
| indexdate | 2024-07-20T09:18:48Z |
| institution | BVB |
| isbn | 9783527406050 3527406050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015694707 |
| oclc_num | 181925505 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-20 DE-703 DE-824 DE-1046 DE-634 DE-92 DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-20 DE-703 DE-824 DE-1046 DE-634 DE-92 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XXX, 819 S. Ill., zahlr. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Handbook of chaos control ed. by Eckehard Schöll ... 2., completely rev. and enl. ed. Weinheim Wiley-VCH 2008 XXX, 819 S. Ill., zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaotic behavior in systems Nonlinear control theory Steuerung (DE-588)4057472-6 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Steuerung (DE-588)4057472-6 s DE-604 Chaostheorie (DE-588)4009754-7 s Kontrolltheorie (DE-588)4032317-1 s 1\p DE-604 Schöll, Eckehard 1951- (DE-588)11019019X edt 1. Aufl. u.d.T. Handbook of chaos control / Heinz Georg Schuster text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2945695&prov=M&dok_var=1&dok_ext=htm Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015694707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Handbook of chaos control Chaotic behavior in systems Nonlinear control theory Steuerung (DE-588)4057472-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Chaostheorie (DE-588)4009754-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4057472-6 (DE-588)4032317-1 (DE-588)4009754-7 (DE-588)4316104-2 |
| title | Handbook of chaos control |
| title_auth | Handbook of chaos control |
| title_exact_search | Handbook of chaos control |
| title_exact_search_txtP | Handbook of chaos control |
| title_full | Handbook of chaos control ed. by Eckehard Schöll ... |
| title_fullStr | Handbook of chaos control ed. by Eckehard Schöll ... |
| title_full_unstemmed | Handbook of chaos control ed. by Eckehard Schöll ... |
| title_old | Handbook of chaos control / Heinz Georg Schuster |
| title_short | Handbook of chaos control |
| title_sort | handbook of chaos control |
| topic | Chaotic behavior in systems Nonlinear control theory Steuerung (DE-588)4057472-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Chaostheorie (DE-588)4009754-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Chaotic behavior in systems Nonlinear control theory Steuerung Kontrolltheorie Chaostheorie Chaotisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2945695&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015694707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scholleckehard handbookofchaoscontrol |