Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems

Jean-René Chazottes, Bastien Fernandez (auth.)3540242899, 9783540242895

This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.

Table of contents :
The CML2004 Project….Pages 1-8
Coupled Map Lattices: at the Age of Maturity….Pages 9-32
On Phase Transitions in Coupled Map Lattices….Pages 33-64
Indecomposable Coupled Map Lattices with Non–unique Phase….Pages 65-94
SRB-Measures for Coupled Map Lattices….Pages 95-114
A Spectral Gap for a One-dimensional Lattice of Coupled Piecewise Expanding Interval Maps….Pages 115-151
Some Topological Properties of Lattice Dynamical Systems….Pages 153-179
Riddled Basins and Coupled Dynamical Systems….Pages 181-207
The Frenkel–Kontorova Model….Pages 209-240
Spatially Extended Systems with Monotone Dynamics (Continuous Time)….Pages 241-263
Spatially Extended Monotone Mappings….Pages 265-284
Desynchronization and Chaos in the Kuramoto Model….Pages 285-306
Modeling the Dynamics of Genetic Regulatory Networks: Continuous and Discrete Approaches….Pages 307-340
Waves and Oscillations in Networks of Coupled Neurons….Pages 341-357