Nonlinear Fokker-Planck Equations Fundamentals and Applications
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equatio
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in Synergetics Series Editor Hermann Haken Institut f¨ur Theoretische Physik und Synergetik der Universit¨at Stuttgart 70550 Stuttgart, Germany and Center for Complex Systems Florida Atlantic University Boca Raton, FL 33431, USA
Members of the Editorial Board Åke Andersson, Stockholm, Sweden Gerhard Ertl, Berlin, Germany Bernold Fiedler, Berlin, Germany Yoshiki Kuramoto, Sapporo, Japan J¨urgen Kurths, Potsdam, Germany Luigi Lugiato, Milan, Italy J¨urgen Parisi, Oldenburg, Germany Peter Schuster, Wien, Austria Frank Schweitzer, Z¨urich, Switzerland Didier Sornette, Los Angeles, CA, USA, and Nice, France Manuel G. Velarde, Madrid, Spain SSSyn – An Interdisciplinary Series on Complex Systems The success of the Springer Series in Synergetics has been made possible by the contributions of outstanding authors who presented their quite often pioneering results to the science community well beyond the borders of a special discipline. Indeed, interdisciplinarity is one of the main features of this series. But interdisciplinarity is not enough: The main goal is the search for common features of self-organizing systems in a great variety of seemingly quite different systems, or, still more precisely speaking, the search for general principles underlying the spontaneous formation of spatial, temporal or functional structures. The topics treated may be as diverse as lasers and fluids in physics, pattern formation in chemistry, morphogenesis in biology, brain functions in neurology or self-organization in a city. As is witnessed by several volumes, great attention is being paid to the pivotal interplay between deterministic and stochastic processes, as well as to the dialogue between theoreticians and experimentalists. All this has contributed to a remarkable cross-fertilization between disciplines and to a deeper understanding of complex systems. The timeliness and potential of such an approach are also mirrored – among other indicators – by numerous interdisciplinary workshops and conferences all over the world.
Till Daniel Frank
Nonlinear Fokker–Planck Equations Fundamentals and Applications
With 86 Figures and 18 Tables
123
Dr. Till Daniel Frank Universit¨at M¨unster Institut f¨ur Theoretische Physik Wilhelm-Klemm-Strasse 9 48149 M¨unster, Germany
ISSN 0172-7389 ISBN 3-540-21264-7 Springer Berlin Heidelberg New York 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. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany
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