Inhalt des Dokuments
Handbook of chaos control
Second completely revised and enlarged edition
849 pages, October 2007 (flyer) (Wiley - VCH)
Editors:
Eckehard Schöll, Technische Universität Berlin
Hans Georg Schuster, Universität Kiel
Preface
During the last decade, control of complex irregular dynamics has evolved as one of the central issues in applied nonlinear science. The number of papers published in this field has been steadily growing since the first pionieering papers appeared in 1990, and has reached an annual number between 600 and 700 during the past few years. The seminal article by Ott, Grebogi, and Yorke (1990), in which they demonstrated that small time dependent changes in the control parameters of a nonlinear system can turn a previously chaotic trajectory into a stable periodic motion, alone was cited much more than 2000 times. Nowadays the notion of chaos control has been extended to a much wider class of problems involving the stabilization of unstable periodic or stationary states in nonlinear dynamic systems. Within the last few years major progress has been made in this field, in particular with respect to
- extending the methods of chaos control to spatio-temporal patterns
- extending the methods of control of deterministic dynamic systems to stochastic and noise-mediated systems
- development of novel control schemes - deepened understanding and analytic insight into different control
schemes - applications to various areas, e.g. biological, medical, technological systems
Since its first publication in 1999, the Handbook on Chaos Control has become the standard reference in this field. Eight years after the first edition, there is need to present the new material which has been accumulated, and to set new trends and identify new promising directions of research.
The present volume is the second completely revised and enlarged edition, and includes only articles which have been newly written for this volume. It aims at presenting a comprehensive overview of the state of the art in this growing field, containing chapters written by the leading scientists who are active in this area. The focus is put on recent developments like novel control schemes, analytical insights, control of chaotic space-time patterns, control of noisy nonlinear systems and noise-induced dynamics, secure communication with chaos, and applications of chaos control to physics, chemistry, biology, medicine, and engineering. Furthermore, the overlap of chaos control with the traditional field of control theory in the engineering community is identified.
The chapters of the book are state-of-the-art review articles and should be of interest to graduate students and researchers; theoretical and experimental physicists, applied mathematicians, electronic engineers, nonlinear scientists from interdisciplinary fields, e.g. chemistry, biology, medicine, control theory, engineering. The 36 chapters are grouped into nine parts, where the first four parts deal with basic aspects
and extension of methods; controlling space-time chaos; controlling noisy motion; communicating with chaos and chaos synchronisation, and the last five parts contain applications to optics, to electronic systems, to chemical reaction systems, to biology and medicine, and to engineering. Among the topics are, for instance, secure communication with chaotic semiconductor lasers, control of communication networks, noninvasive time-delayed feedback control of laser diodes, electronic circuits, and semiconductor nanostructures, control of chemical turbulence and electrochemical oscillators, suppression of synchronisation as therapeutic tools for neural diseases like
Parkinson and epilepsy, and control of cardiac dynamics.
We hope that this volume will stimulate further developments in this still thrilling area which is centered on the overlap of basic research and far-reaching applications.
We would like to thank all authors who have contributed to this volume as well as the publishers for their excellent cooperation. Special thanks are due to Philipp Hövel for his technical assistence.
Berlin and Kiel, June 2007
Eckehard Schöll and Heinz G. Schuster
Table of Contents
A. Basic aspects and extension of methods
1. C. Grebogi, E. Macau (UK): Controlling Chaos
2. J. Socolar (USA): Time-delay control for discrete maps
3. K. Pyragas (Lithuania): An analytical treatment of the delayed feedback
control algorithm
4. B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, E. Schöll (Germany):
Beyond the odd number limitation of time-delayed feedback control
5. W. Just (UK): On global properties of time-delayed feedback control
6. J.C. Claussen (Germany): Poincare-based chaos control of delayed
measured systems: Limitations and Improved Control
7. A. Fradkov, B. Andrievsky (Russia): Nonlinear and adaptive
control of chaos
B. Controlling space-time chaos
8. R. Grigoriev (USA): Localised Control of spatiotemporal chaos
9. S. Boccaletti (Italy): Controlling spatiotemporal chaos
10. U. Parlitz (Germany): Multiple delay feedback control
C. Controlling noisy motion
11. N. Janson, A. Balanov (UK), E. Schöll(Germany):Control of noise-induced
dynamics
12. A. Pikovsky, M. Rosenblum, D. Goldobin (Germany): Controlling
coherence of noisy and chaotic oscillations by delayed feedback
13. C. Masoller (Uruguay): Resonances induced by the delay time in nonlinear
autonomous oscillators with feedback
D. Communicating with chaos, chaos synchronisation
14. W. Kinzel (Würzburg): Secure communication with synchronized
chaotic systems
15. T. L. Carroll (USA): Noise robust chaotic system
16. H. Abarbanel (USA): Nonlinear Communications strategies
17. K.A. Shore (UK): Synchronisation and message transmission for networked
chaotic optical communications
18. J. Kurths (Germany): Feedback control principles for phase
synchronization
E. Applications to optics
19. L. Illing, D. Gauthier (USA): Controlling fast chaos in
opto-electronic delay dynamical systems
20. O. Hess (UK): Control of Broad-Area laser dynamics with Delayed Optical
Feedback
21. H.J. Wünsche (Germany): Noninvasive control of semiconductor lasers
by delayed optical feedback
22. J. Ohtsubo (Japan): Chaos and control in semiconductor lasers
23. B. Gütlich, C. Denz (Germany): From pattern control to synchronisation:
control techniques in nonlinear optical feedback systems
F. Applications to electronic systems
24. E. Schöll (Germany): Delayed feedback control of chaotic spatiotemporal
patterns in semiconductor nanostructures
25. H. Benner (Germany), W. Just (UK): Observing global properties of
time-delayed feedback control in electronic circuits
26. A. Kittel (Germany): Application of a Black Box Strategy to Chaos Control
G. Applications to chemical reaction systems
27. H. Engel (Germany): Feedback-mediated control of hypermeandering spiral
waves
28. A. Mikhailov, C. Beta (Germany): Control of spatiotemporal chaos in
surface chemical reactions
29. J. L. Hudson, I.Z. Kiss (USA): Forcing and feedback control of arrays of
chaotic electrochemical oscillators
H. Applications to biology
30. P. Tass, O. Popovych, Ch. Hauptmann (Germany): Chaos synchronisation in
oscillatory neural networks
31. D. Christini(USA):control of cardiac electrical nonlinear dynamics,
32. Sitabhra Sinha (India): Controlling Spatiotemporal chaos and spiral
turbulence in excitable media
I. Applications to engineering
33. H. Nijmeijer (Netherlands), H. Huijberts (London, UK): Nonlinear
chaos control and synchronization
34. M. Ogorzalek (Poland): Electronic chaos controllers - from theory to
applications
35. E. Mosekilde, Zh. Zhusubaliyev (Denmark): chaos in pulse width
modulated control systems
36. T. Hikihara (Kyoto, Japan): Transient dynamics of Duffing system under
Time Delayed Feedback Control: Global phase structure and
Application to Engineering