E-Book 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.
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This page intentionally left blank Synchronization A universal concept in nonlinear sciences First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering, and social life. 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; 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 the synchronization of periodic oscillators and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering, and natural sciences. A RKADY P IKOVSKY was part of the Max-Planck research group on nonlinear dynamics before becoming Professor of Statistical Physics and Theory of Chaos 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 Review E, for the term 2000–2002. Before this, he was a Humboldt fellow at the University of Wuppertal. His PhD focused 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. M ICHAEL ROSENBLUM has been a research associate in the Department of Physics, University of Potsdam, 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 in the Max-Planck research group on nonlinear dynamics, and a visiting scientist at Boston University. Michael Rosenblum studied physics at Moscow Pedagogical University, and went on to work in the Mechanical Engineering Research Institute of the USSR Academy of Sciences, where he was awarded a PhD in physics and mathematics. ii ¨ J URGEN K URTHS has been Professor of Nonlinear Dynamics at the University of Potsdam and director of the Interdisciplinary Centre for Dynamics of Complex Systems since 1994. He is a fellow of the American Physical Society and fellow of the Fraunhofer Society (Germany), and is currently vice-president of the European Geophysical Society. He is also a member of the Editorial Board of the International Journal of Bifurcation and Chaos. Professor Kurths was director of the group for nonlinear dynamics of th