| Preface | p. ix |
| What are natural patterns? | p. 1 |
| Convection | p. 3 |
| Reaction-diffusion systems | p. 12 |
| Faraday waves | p. 20 |
| Outline of the rest of the book | p. 22 |
| A bit of bifurcation theory | p. 23 |
| Flows, stationary points and periodic orbits | p. 23 |
| Local bifurcations from stationary points | p. 30 |
| Normal forms for bifurcations | p. 38 |
| Codimension-one bifurcations | p. 38 |
| A bit of group theory | p. 52 |
| Groups | p. 52 |
| Subgroups, quotient groups and conjugacy | p. 57 |
| Mappings of groups | p. 61 |
| Products of groups | p. 64 |
| Lie groups | p. 67 |
| Representations of groups | p. 68 |
| Characters | p. 77 |
| Isotypic decomposition | p. 82 |
| Bifurcations with symmetry | p. 85 |
| Ordinary differential equations with spatial symmetry | p. 85 |
| The equivariant branching lemma | p. 93 |
| Bifurcations in a box | p. 97 |
| Hopf bifurcations with symmetry | p. 116 |
| Heteroclinic cycles | p. 122 |
| Appendix: Proofs | p. 131 |
| Simple lattice patterns | p. 134 |
| Lattices and lattice patterns | p. 134 |
| Bifurcations on a lattice | p. 136 |
| Steady bifurcation on a square lattice | p. 141 |
| Steady bifurcation on a hexagonal lattice | p. 147 |
| Roll/stripe solutions | p. 157 |
| The Kuppers-Lortz instability | p. 158 |
| Hopf bifurcation on a one-dimensional lattice | p. 161 |
| Superlattices, hidden symmetries and other complications | p. 168 |
| Superlattice patterns | p. 168 |
| Mode interactions | p. 174 |
| Spatial-period-multiplying bifurcations | p. 178 |
| Quasipatterns | p. 182 |
| Pseudoscalar actions of E(2) | p. 187 |
| Hidden symmetries | p. 190 |
| Hidden symmetries and reflecting boundary conditions | p. 198 |
| Spatial modulation and envelope equations | p. 209 |
| Envelope equations for specific models | p. 209 |
| Envelope equations and symmetries | p. 216 |
| Free energies or Lyapunov functionals | p. 224 |
| Conservation of 'angular momentum' | p. 227 |
| Hopf bifurcations and the complex Ginzburg-Landau equation | p. 232 |
| Travelling waves and the nonlinear Schrodinger equation | p. 234 |
| Modulated hexagons | p. 238 |
| Instabilities of stripes and travelling plane waves | p. 243 |
| Universal instabilities of stripes | p. 243 |
| The Eckhaus instability | p. 247 |
| The zigzag instability | p. 260 |
| A general theory of phase dynamics | p. 266 |
| The cross-roll instability | p. 274 |
| Prandtl-number-dependent instabilities of convection rolls | p. 277 |
| The Benjamin-Feir instability | p. 286 |
| More instabilities of patterns | p. 292 |
| Instabilities of two-dimensional steady patterns | p. 292 |
| Drift instabilities | p. 306 |
| Galilean invariance and flat modes | p. 315 |
| Conservative systems and flat modes | p. 319 |
| Spirals, defects and spiral defect chaos | p. 325 |
| Types of isolated defect | p. 325 |
| Dislocation of a roll pattern | p. 327 |
| Amplitude grain boundaries | p. 337 |
| Domain boundaries between different patterns in systems with a free energy | p. 342 |
| Energetic considerations for rolls in finite domains | p. 349 |
| Spirals | p. 353 |
| Spirals in oscillatory and excitable systems | p. 354 |
| Drifting and meandering spirals | p. 362 |
| Spiral defect chaos | p. 375 |
| Large-aspect-ratio systems and the Cross-Newell equation | p. 380 |
| Fully nonlinear patterns in large-aspect-ratio boxes | p. 381 |
| Stationary solutions of the Cross-Newell equation | p. 388 |
| Defect solutions of the Cross-Newell equation | p. 390 |
| Models with variational structure | p. 400 |
| Systems with mean drift | p. 404 |
| References | p. 408 |
| Index | p. 417 |
| Table of Contents provided by Ingram. All Rights Reserved. |
