Phase Transitions and Synergetics
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nstitute 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
J¨urgen Kurths Nonlinear Dynamics Group, University of Potsdam, Potsdam, Germany
Linda 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 System Design, ETH Zurich, Zurich, Switzerland
Didier Sornette Entrepreneurial Risk, ETH Zurich, Zurich, Switzerland
Understanding Complex Systems Founding Editor: J.A. Scott Kelso
Future scientific and technological developments in many fields will necessarily depend upon coming to grips with complex systems. Such systems are complex in both their composition – typically many different kinds of components interacting simultaneously and nonlinearly with each other and their environments on multiple levels – and in the rich diversity of behavior of which they are capable. The Springer Series in Understanding Complex Systems series (UCS) promotes new strategies and paradigms for understanding and realizing applications of complex systems research in a wide variety of fields and endeavors. UCS is explicitly transdisciplinary. It has three main goals: First, to elaborate the concepts, methods and tools of complex systems at all levels of description and in all scientific fields, especially newly emerging areas within the life, social, behavioral, economic, neuroand cognitive sciences (and derivatives thereof); second, to encourage novel applications of these ideas in various fields of engineering and computation such as robotics, nano-technology and informatics; third, to provide a single forum within which commonalities and differences in the workings of complex systems may be discerned, hence leading to deeper insight and understanding. UCS will publish monographs, lecture notes and selected edited contributions aimed at communicating new findings to a large multidisciplinary audience.
Vladimir G. Ivancevic · Tijana T. Ivancevic
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
With 125 Figures and 1 Table
Dr. Vladimir G. Ivancevic
Dr. Tijana T. Ivancevic
Human Systems Integration Land Operations Division Defence Science & Technology Organisation PO Box 1500, 75 Labs Edinburgh SA 5111 Australia [email protected]
School of Electrical and Information Engineering University of South Australia Mawson Lakes Boulevard Mawson Lakes, S.A. 5095, Australia [email protected]
ISBN: 978-3-540-79356-4
e-ISBN: 978-3-540-79357-1
Understanding Complex Systems ISSN: 1860-0832 Library of Congress Control Number: 2008925879 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part
