Synchronization From Simple to Complex

Synchronization: From Simple to Complex is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, fro

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Programme Advisory Board Péter Érdi Center for Complex Systems Studies, Kalamazoo College, USA, and Hungarian Academy of Sciences, Budapest, Hungary

Karl J. Friston Institute of Cognitive Neuroscience, University College London, London, UK

Hermann Haken Center of Synergetics, University of Stuttgart, Stuttgart, Germany

Janusz Kacprzyk System Research, Polish Academy of Sciences, Warsaw, Poland

Scott Kelso Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, USA

Jürgen Kurths Nonlinear Dynamics Group, University of Potsdam, Potsdam, Germany

Linda E. Reichl Center for Complex Quantum Systems, University of Texas, Austin, USA

Peter Schuster Theoretical Chemistry and Structural Biology, University of Vienna, Vienna, Austria

Frank Schweitzer Systems Design, ETH Zurich, Zurich, Switzerland

Didier Sornette Entrepreneurial Risk, ETH Zurich, Zurich, Switzerland

Springer Series in Synergetics Founding Editor: H. Haken The Springer Series in Synergetics was founded by Herman Haken in 1977. Since then, the series has evolved into a substantial reference library for the quantitative, theoretical and methodological foundations of the science of complex systems. Through many enduring classic texts, such as Haken’s Synergetics and Information and SelfOrganization, Gardiner’s Handbook of Stochastic Methods, Risken’s The Fokker Planck-Equation or Haake’s Quantum Signatures of Chaos, the series has made, and continues to make, important contributions to shaping the foundations of the field. The series publishes monographs and graduate-level textbooks of broad and general interest, with a pronounced emphasis on the physico-mathematical approach.

Alexander Balanov, Natalia Janson, Dmitry Postnov, Olga Sosnovtseva

Synchronization From Simple to Complex With 150 Figures

Dr. Alexander Balanov

Dr. Natalia Janson

Loughborough University Department of Physics Loughborough Leicestershire LE11 3TU United Kindom [email protected]

Loughborough University School of Mathematics Ashby Road Loughborough Leicestershire LE11 3TU United Kingdom [email protected]

Prof. Dmitry Postnov

Dr. Olga Sosnovtseva

Saratov State University Department of Physics Astrakhanskaya 83 Saratov, Russia 410026 [email protected]

Technical University of Denmark Department of Physics Building 309 2800 Lyngby, Denmark [email protected]

ISBN 978-3-540-72127-7

e-ISBN 978-3-540-72128-4

DOI 10.1007/978-3-540-72128-4 Library of Congress Control Number: 2008929606 © 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer