Overview

This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community. An interdisciplinary approach of interest to scientists and engineers working in a number of areas.

Full Product Details

Author:   Eckehard Schöll (Technical University of Berlin, Germany) ,  Heinz Georg Schuster (Institute of Theoretical Physics and Astrophysics)
Publisher:   Wiley-VCH Verlag GmbH
Imprint:   Blackwell Verlag GmbH
Edition:   2nd edition
Dimensions:   Width: 17.30cm , Height: 4.60cm , Length: 24.60cm
Weight:   1.687kg
ISBN:  

9783527406050

ISBN 10:   3527406050
Pages:   849
Publication Date:   24 October 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of 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 Grebogi 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 13 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 3 An Analytical Treatment of the Delayed Feedback Control Algorithm 47 Kestutis Pyragas, Tatjana Pyragienė, 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 Rössler 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 Controlled by Delayed Feedback 60 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 Georgi, Philipp Hövel, and Eckehard Schöll 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 Acknowledgments 102 Appendix A. Normal Form Reduction 103 Appendix B. Super- and Subcritical Hopf Bifurcation for Maps 106 References 106 6 Poincaré-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 Schemes 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 Hénon System 144 7.3.6 Feedback Linearization Control of the Lorenz System 146 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 Rössler 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. Grigoriev 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 of MDFC 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 G. Balanov, and Eckehard Schöll 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 Controlled 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 Goldobin, 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 Asymmetric 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 Rössler 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 Rössler 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 Ilestyn 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 17.4 Summary 376 Acknowledgments 376 References 376 18 Feedback Control Principles for Phase Synchronization 379 Vladimir N. Belykh, Grigory V. Osipov, and Jürgen Kurths 18.1 Introduction 379 18.2 General Principles of Automatic Synchronization 381 18.3 Two Coupled Poincaré Systems 384 18.4 Coupled van der Pol and Rössler Oscillators 386 18.5 Two Coupled Rössler Oscillators 389 18.6 Coupled Rössler and Lorenz Oscillators 391 18.7 Principles of Automatic Synchronization in Networks of Coupled Oscillators 393 18.8 Synchronization of Locally Coupled Regular 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 Illing, Daniel J. Gauthier, 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 Gaciu, 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 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-Jürgen Wünsche, 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 23 From Pattern Control to Synchronization: Control Techniques in Nonlinear Optical Feedback Systems 501 Björn Gütlich 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 Schöll 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 Benner, Chol-Ung Choe, Klaus Höhne, 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 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(110) 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(110) 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 István 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 X=x 0 637 29.2.3.2 Forcing with X 6ˆ X 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 Multisite 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 David J. Christini 31.1 Introduction 683 31.2 Cardiac Electrophysiology 684 31.2.1 Restitution and Alternans 685 31.3 Cardiac Arrhythmias 686 31.3.1 Reentry 687 31.3.2 Ventricular Tachyarrhythmias 688 31.3.3 Alternans 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 Alternans Control 691 31.5.1 Controlling Cellular Alternans 691 31.5.2 Control of Alternans in Tissue 692 31.5.3 Limitations of the DFC Algorithm in Alternans 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 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 Geometric Control 721 33.2.1 Some Differential Geometric 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 Lyapunov’s 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 Ogorzałek 34.1 Introduction 751 34.1.1 Chaos Control 752 34.1.2 Fundamental Properties of Chaotic Systems and Goals of the 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 

Reviews

The book is interdisciplinary and can be of interest to graduate students, researchers in different fields: physicists, mathematicians and, engineers. ( Zentralblatt MATH , 1132, 2008)

The book is interdisciplinary and can be of interest to graduate students, researchers in different fields: physicists, mathematicians and, engineers. (Zentralblatt MATH, 1132, 2008)

Author Information

Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. In 1971 he received his doctorate and in 1976 he was appointed Professor at the University of Frankfurt/Main in Germany. He was a visiting professor at the Weizmann-Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. Professor Schuster works on the dynamical behaviour of complex adaptive systems and authored and coauthored several books in this field. His book ""Deterministic Chaos"" which was also published at Wiley-VCH, has been translated into five languages. Eckehard Scholl received his M.Sc. in physics from the University of Tuebingen, Germany, and his Ph.D. degree in applied mathematics from the University of Southampton, England. In 1989 he was appointed to a professorship in theoretical physics at the Technical University of Berlin, where he still teaches. His research interests are nonlinear dynamic systems, including nonlinear spatio-temporal dynamics, chaos, pattern formation, noise, and control. He authored and coauthored several books in his field. Professor Scholl was awarded the ""Champion in teaching"" prize by the Technical University of Berlin in 1997 and a Visiting Professorship by the London Mathematical Society in 2004.

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