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Patterns of Dynamics

Berlin, July 2016

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Pavel Gurevich

    1. Mathematical Institute, Free University of Berlin, Berlin, Germany

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  2. Juliette Hell

    1. Mathematical Institute, Free University of Berlin, Berlin, Germany

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  3. Björn Sandstede

    1. Division of Applied Mathematics, Brown University, Providence, USA

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  4. Arnd Scheel

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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  • Discusses theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering
  • Builds and develops mathematical techniques, and uses mathematical approaches for prediction and control of complex systems

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 205)

Included in the following conference series:

Conference proceedings info: PaDy 2016.

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About this book

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes. 


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Table of contents (21 papers)

  1. Front Matter

    Pages i-ix
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  2. Patterns and Waves

    1. Front Matter

      Pages 1-1
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    2. Uniqueness of Solitary Waves in the High-Energy Limit of FPU-Type Chains

      • Michael Herrmann, Karsten Matthies
      Pages 3-15

    3. Patterns in Fourier Space

      • Jürgen Scheurle
      Pages 16-27

    4. The Turing Instability in Case of an Additional Conservation Law—Dynamics Near the Eckhaus Boundary and Open Questions

      • Guido Schneider, Dominik Zimmermann
      Pages 28-43

    5. Noise-Induced Chimera States in a Neural Network

      • Anna Zakharova, Nadezhda Semenova, Vadim Anishchenko, Eckehard Schöll
      Pages 44-63

  3. Statistical Properties of Dynamics

    1. Front Matter

      Pages 65-65
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    2. A Survey on the Fourier Dimension

      • Fredrik Ekström, Jörg Schmeling
      Pages 67-87

    3. Depinning Asymptotics in Ergodic Media

      • Arnd Scheel, Sergey Tikhomirov
      Pages 88-108

  4. Nonlinear Partial Differential Equations

    1. Front Matter

      Pages 109-109
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    2. An Implicit Function Theorem and Applications to Nonsmooth Boundary Layers

      • Valentin Fëdorovich Butuzov, Nikolai N. Nefedov, Oleh E. Omel’chenko, Lutz Recke, Klaus R. Schneider
      Pages 111-127

    3. Existence and Exact Multiplicity for Quasilinear Elliptic Equations in Quarter-Spaces

      • Yihong Du, Messoud Efendiev
      Pages 128-137

    4. Non-uniqueness of Solutions of a Semilinear Heat Equation with Singular Initial Data

      • Marek Fila, Hiroshi Matano, Eiji Yanagida
      Pages 138-148

    5. Uniform Exponential Decay for Reaction-Diffusion Systems with Complex-Balanced Mass-Action Kinetics

      • Alexander Mielke
      Pages 149-171

    6. Convergence and Quasiconvergence Properties of Solutions of Parabolic Equations on the Real Line: An Overview

      • Peter Poláčik
      Pages 172-183

    7. Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings

      • Lutz Recke, Martin Väth, Milan Kučera, Josef Navrátil
      Pages 184-202

    8. Enumeration of Positive Meanders

      • Matthias Wolfrum
      Pages 203-212

  5. Control and Numerics

    1. Front Matter

      Pages 213-213
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    2. Freezing Traveling and Rotating Waves in Second Order Evolution Equations

      • Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes
      Pages 215-241

    3. Numerical Center Manifold Methods

      • Klaus Böhmer
      Pages 242-268
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Other volumes

  1. Patterns of Dynamics

Editors and Affiliations

  • Mathematical Institute, Free University of Berlin, Berlin, Germany

    Pavel Gurevich, Juliette Hell

  • Division of Applied Mathematics, Brown University, Providence, USA

    Björn Sandstede

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Arnd Scheel

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