Synchronization: A Universal Concept in Nonlinear Sciences

by Arkady Pikovsky, Michael Rosenblum, Jürgen Kurths

Overview

Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is also outlined. The second half of the book presents the main effects of synchronization in a rigorous and systematic manner, describing both classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media.

Product Details

ISBN-13:	9780521533522
Publisher:	Cambridge University Press
Publication date:	04/24/2003
Series:	Cambridge Nonlinear Science Series , #12
Edition description:	1ST
Pages:	432
Product dimensions:	6.69(w) x 9.57(h) x 0.94(d)

About the Author

Arkady Pikovsky was part of the Max-Planck research group on nonlinear dynamics, before becoming a professor at the University of Potsdam, Germany. A member of the German and American Physical Societies, he is also part of the Editorial Board of Physical Reviews E for the term 2000-2002. Before this, he was a Humboldt fellow at University of Wuppertal. His PhD focusses on the theory of chaos and nonlinear dynamics, and was carried out at the Institute of Applied Physics of the USSR Academy of Sciences. Arkady Pikovsky studied radiophysics and physics at Gorky State University, and started to work on chaos in 1976, describing an electronic device generating chaos in his Diploma thesis and later proving it experimentally.

Professor Michael Rosenblum has been a research associate in Department of Physics, Potsdam University since 1997. His main research interests are the application of oscillation theory and nonlinear dynamics to biological systems and time series analysis. He was a Humboldt fellow at the Max-Planck research group on non-linear dynamics, and a visiting scientist at Boston University. Professor Rosenblum studied physics at Moscow Pedagogical University, and went on to work in the Mechanical Engineering Research Institute of USSR Academy of Sciences, obtaining a PhD in physics and mathematics.

Jurgen Kurths has been professor at the University of Potsdam and director of the Interdisciplinary Centre for Nonlinear Dynamics since 1994. He is a fellow of the American Physical Society and fellow of the Fraunhofer Society (Germany), and is currently the chairman for Nonlinear Processes in Geophysics and member of the council in Geophysics of the European Geophysical Society. In 2001 he will be a member of the Editorial Board of the Int. J. of Bifurcation and Chaos. Professor Kurths was director of the group for Nonlinear Dynamics of the Max-Planck Society from 1992–1996. He studied mathematics at Rostock University, and then went on to work at the Solar-Terrestrial Physics Institute, and later the Astrophysical Institute of GDR Academy of Sciences. He obtained his PhD in Physics, and started to work on nonlinear data analysis and chaos in 1984. His main research interests are nonlinear dynamics and their applications to geophysics and physiology and to time series analysis.

Table of Contents

Preface; 1. Introduction; Part I. Synchronization Without Formulae: 2. Basic notions: the self-sustained oscillator and its phase; 3. Synchronization of a periodic oscillator by external force; 4. Synchronization of two and many oscillators; 5. Synchronization of chaotic systems; 6. Detecting synchronization in experiments; Part II. Phase Locking and Frequency Entrainment: 7. Synchronization of periodic oscillators by periodic external action; 8. Mutual synchronization of two interacting periodic oscillators; 9. Synchronization in the presence of noise; 10. Phase synchronization of chaotic systems; 11. Synchronization in oscillatory media; 12. Populations of globally coupled oscillators; Part III. Synchronization of Chaotic Systems: 13. Complete synchronization I: basic concepts; 14. Complete synchronization II: generalizations and complex systems; 15. Synchronization of complex dynamics by external forces; Appendix 1. Discovery of synchronization by Christiaan Huygens; Appendix 2. Instantaneous phase and frequency of a signal; References; Index.

Editorial Reviews

"This attractively laid-out book contains numerous fascinating examples of synchronization culled from the physical and biological sciences...The book concludes with one of the best expositions on the synchronization of chaotic systems that I have read...Clearly, the authors...have pulled off a very difficult trick, that of writing a book that is both a definitive introduction to synchronization for the casual reader and a definitive text for researchers working in a variety of fields." Nature

"This book will be of use to anybody interested or working in the field. It should find its place on the shelves of many science libraries because it supplies sufficient resources to both the layperson and the specialist." Pure Applicational Geophysics

"This book includes bountiful examples...Synchronization is most suited...for graduate students in the sciences, engineering or mathematics and other scientists who want to learn about this exciting and rapidly developing field." Rober C. Hilborn, American Association of Physics Teachers

"Synchronization is the first book to treat this subject in a unified fashion...an unconventional but excellent pedagogical choice...the treatment of the fundamentals is very well done and more readable than much of the original literature on this still-fashionable subject." Physics Today January 2003

"This book will be of use to anybody interested or working in the field. It should find its place on the shelves of many science libraries because it supplies sufficient resources to both the layperson and the specialist." Pure Applicational Geophysics

From the Publisher