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Handbook of Chaos Control [Kõva köide]

  • Formaat: Hardback, 706 pages, kõrgus x laius: 245x172 mm, kaal: 1500 g, Illustrationssome col.)
  • Ilmumisaeg: 24-Mar-1999
  • Kirjastus: Wiley-VCH Verlag GmbH
  • ISBN-10: 3527294368
  • ISBN-13: 9783527294367
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  • Formaat: Hardback, 706 pages, kõrgus x laius: 245x172 mm, kaal: 1500 g, Illustrationssome col.)
  • Ilmumisaeg: 24-Mar-1999
  • Kirjastus: Wiley-VCH Verlag GmbH
  • ISBN-10: 3527294368
  • ISBN-13: 9783527294367
Teised raamatud teemal:
Summarizes the current state in taking advantage of the sensitive dependence of a chaotic system to control its irregular dynamic behavior with a minimum of additional energy. After an introduction to chaos theory itself, describes all known methods of chaos control for a number of different type systems, among them controlling patterns and spatiotemporal chaos, spatially extended chaotic systems, topological defects, transient chaos on chaotic saddles, and periodic orbit theory for classical chaotic systems. Much of the text is concerned with applications, which include electronic circuits, lasers and chemical plants, and the anti-chaos control in biological systems that offers the possibility of avoiding epileptic seizures. The book shows the title and ISBN as indicated above, but Books in Print shows confusion about the ISBN (it's connected with an entirely different book); and Wiley's customer service department reports a variant title: Control of Chaos; From Theory to Application. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Chaos, that is irregular dynamical behaviour, is ubiquituous in nature and occurs in a wide range of systems including lasers, fluids, etc., heart beats and brain waves. Before 1990 the emergence of chaos in a system was mostly considered as a nuisance because chaotic systems are hard to predict due to their sensitivity to small perturbations. After 1990 it became clear that this sensitive dependence offers the unique possibility to control these systems with a minimum of additional energy.

This handbook provides a comprehensive up-to-date overview of the field. It starts with an introduction to chaos theory, and covers all known methods of chaos control from parametric feedback to neuronal networks. A large part of the handbook is devoted to applications which range from control of electronic circuits, the control of lasers and chemical plants up to "antichaos control" in biological systems which offers the possibility to avoid epileptic seizures.

Arvustused

"It can certainly be recommended. The work is reasonably current, containing a wealth of applications and an extensive guide to the literature." (Pure & Applied Geophysics)

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