Preface | p. vii |
Patterns: Prelude to a Dynamical Description | p. 1 |
Linear Stage of Pattern Formation | p. 15 |
Model Equations | p. 27 |
Swift--Hohenberg equation | p. 29 |
Newell--Whitehead--Segel equation | p. 35 |
Coupled amplitude equations | p. 38 |
Phase equations | p. 42 |
The Ginzburg--Landau Equation | p. 45 |
The dissipative Ginzburg--Landau equation | p. 46 |
Nerve membrane excitation and the CGL equation | p. 48 |
Optical dynamics and the CGL equation | p. 50 |
Simple patterns in the CGL equation | p. 52 |
Phase equations revisited | p. 55 |
Gallery of phenomena | p. 57 |
'Crystal' Formation | p. 63 |
Quasicrystals | p. 75 |
Octagons, decagons, and dodecagons | p. 78 |
A generalized Swift-Hohenberg model | p. 81 |
The 'turbulent' crystal | p. 82 |
Breaking of Order | p. 87 |
A simple model for domain walls | p. 89 |
Topological defects | p. 92 |
The birth of penta-hepta defects | p. 96 |
Dislocations and domain walls in Faraday ripples | p. 102 |
Localized Patterns | p. 107 |
Bistable media | p. 107 |
Dynamical disorder of structures | p. 114 |
Particle interaction | p. 115 |
Chaotic scattering | p. 118 |
Spirals | p. 129 |
Active spirals | p. 133 |
Spirals in the complex Ginzburg--Landau equation | p. 133 |
Spirals in the FitzHugh-Nagumo model | p. 136 |
Passive spirals | p. 142 |
Spirals in the Faraday experiment | p. 143 |
Spirals in Rayleigh-Benard convection | p. 145 |
Patterns in Oscillating Soap Films | p. 151 |
Introduction | p. 151 |
Observations | p. 152 |
Models for vorticity generation | p. 158 |
Marangoni wave model | p. 160 |
The role of air | p. 162 |
Patterns in Colonies of Microorganisms | p. 173 |
Dictyostelium discoideum | p. 174 |
Esherichia coli | p. 178 |
Bacillus subtilis | p. 184 |
Spatial Disorder | p. 189 |
Introductory remarks | p. 189 |
Characteristics of space series | p. 193 |
The Grassberger-Procaccia algorithm | p. 197 |
Qualitative description of developing disorder | p. 199 |
Dynamical dimension of defect-mediated turbulence | p. 202 |
Patterns in Chaotic Media | p. 205 |
Introductory remarks | p. 205 |
Chaotic synchronization | p. 208 |
Coexistence of regular patterns and chaos | p. 211 |
Coarse grain spatio-temporal patterns | p. 214 |
Coherent patterns on a chaotic checkerboard | p. 220 |
Epilogue: Living matter and dynamic forms | p. 225 |
Hallucinations | p. 227 |
Spatio-temporal patterns and information processing | p. 234 |
A Short Guide to Nonlinear Dynamics | p. 239 |
Dynamical systems | p. 239 |
Types of dynamical systems | p. 240 |
Equilibrium states | p. 241 |
Homoclinic and heteroclinic trajectories | p. 245 |
Limit cycles | p. 248 |
Quasiperiodic motion | p. 249 |
Bifurcations | p. 250 |
Bifurcations of equilibrium states | p. 252 |
Birth of periodic motions | p. 258 |
Change of stability in periodic motions | p. 260 |
Chaotic Oscillations | p. 261 |
Characteristics of chaos and the strange attractor | p. 261 |
Chaotic Hamiltonian systems | p. 263 |
Chaotic self-excited oscillations | p. 264 |
Synchronization of oscillations | p. 266 |
Dynamical chaos and turbulence | p. 271 |
Key Experiments in Pattern Formation | p. 279 |
Parametrically excited patterns | p. 279 |
Experiments with liquids | p. 279 |
Experiments with granular material | p. 287 |
Thermal convection | p. 292 |
Rayleigh-Benard convection | p. 292 |
Patterns in Rayleigh-Benard convection | p. 295 |
Benard-Marangoni convection | p. 297 |
Diffusive chemical reactions | p. 302 |
Turing patterns | p. 302 |
Oscillating chemical reactions | p. 306 |
Bibliography | p. 309 |
Index | p. 320 |
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