Patterns of Dynamics

Part I. Patterns and Waves

1. Uniqueness of Solitary Waves in the High-Energy Limit of FPU-Type Chains
Michael Herrmann, Karsten Matthies

2. Patterns in Fourier Space
Jürgen Scheurle

3. The Turing Instability in Case of an Additional Conservation Law—Dynamics Near the Eckhaus Boundary and Open Questions
Guido Schneider, Dominik Zimmermann

4. Noise-Induced Chimera States in a Neural Network
Anna Zakharova, Nadezhda Semenova, Vadim Anishchenko, Eckehard Schöll

Part II. Statistical Properties of Dynamics

5. A Survey on the Fourier Dimension
Fredrik Ekström, Jörg Schmeling

6. Depinning Asymptotics in Ergodic Media
Arnd Scheel, Sergey Tikhomirov

Part III. Nonlinear Partial Differential Equations

7. 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

8. Existence and Exact Multiplicity for Quasilinear Elliptic Equations in Quarter-Spaces
Yihong Du, Messoud Efendiev

9. Non-uniqueness of Solutions of a Semilinear Heat Equation with Singular Initial Data
Marek Fila, Hiroshi Matano, Eiji Yanagida

10. Uniform Exponential Decay for Reaction-Diffusion Systems with Complex-Balanced Mass-Action Kinetics
Alexander Mielke

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

12. Crandall-Rabinowitz Type Bifurcation for Non-differentiable Perturbations of Smooth Mappings
Lutz Recke, Martin Väth, Milan Kučera, Josef Navrátil

13. Enumeration of Positive Meanders
Matthias Wolfrum

Part IV. Control and Numerics

14. Freezing Traveling and Rotating Waves in Second Order Evolution Equations
Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes

15. Numerical Center Manifold Methods
Klaus Böhmer

16. An Introduction to the Control Triple Method for Partial Differential Equations
Isabelle Schneider

Part V. Applications—Biology and Data Science

17. Data Mining When Each Data Point is a Network
Karthikeyan Rajendran, Assimakis Kattis, Alexander Holiday, Risi Kondor, Ioannis G. Kevrekidis

18. A Calvin Bestiary
Alan D. Rendall

19. “Big Data and Dynamics”—The Mathematical Toolkit Towards Personalized Medicine
Lisa Turnhoff, Nina Kusch, Andreas Schuppert

20. Using Dynamics to Analyse Time Series
Sjoerd Verduyn Lunel

21. Unraveling the Dynamics of the Brain through Modeling and Analysis
Lai-Sang Young

Keywords: Mathematics, Dynamical Systems and Ergodic Theory, Partial Differential Equations, Ordinary Differential Equations, Applications of Mathematics