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| Preface | |
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| What are natural patterns? | |
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| Convection | |
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| Reaction-diffusion systems | |
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| Faraday waves | |
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| Outline of the rest of the book | |
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| A bit of bifurcation theory | |
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| Flows, stationary points and periodic orbits | |
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| Local bifurcations from stationary points | |
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| Normal forms for bifurcations | |
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| Codimension-one bifurcations | |
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| A bit of group theory | |
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| Groups | |
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| Subgroups, quotient groups and conjugacy | |
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| Mappings of groups | |
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| Products of groups | |
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| Lie groups | |
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| Representations of groups | |
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| Characters | |
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| Isotypic decomposition | |
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| Bifurcations with symmetry | |
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| Ordinary differential equations with spatial symmetry | |
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| The equivariant branching lemma | |
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| Bifurcations in a box | |
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| Hopf bifurcations with symmetry | |
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| Heteroclinic cycles | |
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| Appendix: Proofs | |
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| Simple lattice patterns | |
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| Lattices and lattice patterns | |
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| Bifurcations on a lattice | |
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| Steady bifurcation on a square lattice | |
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| Steady bifurcation on a hexagonal lattice | |
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| Roll/stripe solutions | |
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| The Kuppers-Lortz instability | |
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| Hopf bifurcation on a one-dimensional lattice | |
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| Superlattices, hidden symmetries and other complications | |
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| Superlattice patterns | |
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| Mode interactions | |
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| Spatial-period-multiplying bifurcations | |
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| Quasipatterns | |
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| Pseudoscalar actions of E(2) | |
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| Hidden symmetries | |
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| Hidden symmetries and reflecting boundary conditions | |
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| Spatial modulation and envelope equations | |
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| Envelope equations for specific models | |
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| Envelope equations and symmetries | |
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| Free energies or Lyapunov functionals | |
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| Conservation of 'angular momentum' | |
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| Hopf bifurcations and the complex Ginzburg-Landau equation | |
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| Travelling waves and the nonlinear Schrodinger equation | |
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| Modulated hexagons | |
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| Instabilities of stripes and travelling plane waves | |
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| Universal instabilities of stripes | |
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| The Eckhaus instability | |
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| The zigzag instability | |
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| A general theory of phase dynamics | |
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| The cross-roll instability | |
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| Prandtl-number-dependent instabilities of convection rolls | |
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| The Benjamin-Feir instability | |
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| More instabilities of patterns | |
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| Instabilities of two-dimensional steady patterns | |
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| Drift instabilities | |
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| Galilean invariance and flat modes | |
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| Conservative systems and flat modes | |
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| Spirals, defects and spiral defect chaos | |
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| Types of isolated defect | |
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| Dislocation of a roll pattern | |
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| Amplitude grain boundaries | |
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| Domain boundaries between different patterns in systems with a free energy | |
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| Energetic considerations for rolls in finite domains | |
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| Spirals | |
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| Spirals in oscillatory and excitable systems | |
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| Drifting and meandering spirals | |
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| Spiral defect chaos | |
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| Large-aspect-ratio systems and the Cross-Newell equation | |
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| Fully nonlinear patterns in large-aspect-ratio boxes | |
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| Stationary solutions of the Cross-Newell equation | |
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| Defect solutions of the Cross-Newell equation | |
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| Models with variational structure | |
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| Systems with mean drift | |
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| References | |
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| Index | |