| Introduction | p. 1 |
| Quest for Complexity | p. 1 |
| Conservative and Dissipative Systems | p. 2 |
| Closed and Open Systems | p. 3 |
| Field Variables | p. 4 |
| Historical and Bibliographical Notes | p. 6 |
| Dynamics, Stability and Bifurcations | p. 9 |
| Basic Models | p. 9 |
| Dynamical Systems | p. 9 |
| Reaction-Diffusion System | p. 13 |
| Vertical Structure and Representative Equations | p. 15 |
| Spectral Decompositions | p. 17 |
| Trajectories and Attractors | p. 19 |
| Linear Analysis | p. 21 |
| Instabilities of Stationary States | p. 21 |
| Turing and Hopf Instabilities | p. 23 |
| Dispersion Relations | p. 24 |
| Instabilities of Periodic Orbits | p. 25 |
| Weakly Nonlinear Analysis | p. 27 |
| Multiscale Expansion | p. 27 |
| Bifurcation of Stationary States | p. 29 |
| Derivation of Amplitude Equations | p. 32 |
| Hopf Bifurcation | p. 35 |
| Degenerate Bifurcations | p. 38 |
| Global Bifurcations | p. 39 |
| Global Dynamics: An Overview | p. 39 |
| Systems with Separated Time Scales | p. 42 |
| Almost Hamiltonian Dynamics | p. 45 |
| Bifurcation Diagrams | p. 46 |
| Deterministic Chaos | p. 51 |
| Chaotic Attractors | p. 51 |
| Shilnikov Bifurcation | p. 54 |
| Period Doubling Cascade | p. 57 |
| Lorenz System | p. 61 |
| Dynamics of Planforms | p. 66 |
| Interaction of Turing Modes | p. 66 |
| Resonant Planforms | p. 69 |
| Degenerate Wave Modes | p. 74 |
| Biscale Resonances | p. 77 |
| Fronts and Interfaces | p. 83 |
| Planar Fronts | p. 83 |
| Space-Dependent Amplitude Equations | p. 83 |
| Propagating Front as a Heteroclinic Trajectory | p. 85 |
| Computation of the Propagation Speed | p. 87 |
| Maxwell Construction | p. 89 |
| Unstable Nonuniform States | p. 90 |
| Front Interactions | p. 91 |
| Weakly Curved Fronts | p. 94 |
| Aligned Coordinate Frame | p. 94 |
| Expansion Near Maxwell Construction | p. 97 |
| Burgers Equation | p. 98 |
| Ripening under Global Control | p. 100 |
| Propagation into an Unstable State | p. 103 |
| Continuum of Propagating Solutions | p. 103 |
| Asymptotic Theory of the Leading Edge | p. 105 |
| Stability of the Leading Edge | p. 106 |
| Pulled and Pushed Fronts | p. 108 |
| Cahn-Hilliard Equation | p. 110 |
| Order Parameter and Energy Functional | p. 110 |
| Conservative Gradient Dynamics | p. 111 |
| Inner and Outer Equations | p. 112 |
| Solvability Condition and Matching | p. 114 |
| Propagation and Coarsening in 1D | p. 117 |
| Ostwald Ripening | p. 121 |
| Phase Field Model | p. 123 |
| Variational Principle for Phase Field Model | p. 123 |
| Sharp Interface Limit | p. 124 |
| Mobility Relation | p. 126 |
| Instabilities of Interphase Boundaries | p. 127 |
| Instabilities due to Coupling to Control Field | p. 127 |
| Mullins-Sekerka Instability | p. 129 |
| Instability of a Curved Interface | p. 132 |
| Directional Solidification | p. 134 |
| Long-Scale Instability | p. 137 |
| Systems with Separated Scales | p. 141 |
| Stationary Structures | p. 141 |
| FitzHugh-Nagumo System | p. 141 |
| Stationary Structures in 1D | p. 143 |
| Solitary Disk and Sphere | p. 145 |
| Migration-Enhanced Structures | p. 148 |
| Quasistationary Dynamics | p. 150 |
| Symmetry Breaking Instabilities | p. 152 |
| Stability of a Straight-Line Front | p. 152 |
| Stability of a Solitary Band | p. 153 |
| Stability of a Striped Pattern | p. 154 |
| Stability of a Solitary Disk and Cylinder | p. 157 |
| Dynamic Instabilities | p. 160 |
| Propagating Fronts | p. 160 |
| Traveling Instability | p. 162 |
| Oscillatory Instability | p. 163 |
| Phenomenological Velocity-Curvature Relation | p. 165 |
| Long-Scale Evolution Equations | p. 170 |
| Locally Induced Motion | p. 172 |
| Intrinsic Equations of Motion | p. 172 |
| Steadily Rotating Spiral | p. 174 |
| Propagation into a Quiescent State | p. 177 |
| Spiral Band near Ising-Bloch Bifurcation | p. 179 |
| Advective Limit | p. 181 |
| Inertial Scaling | p. 181 |
| Dispersion Relation for Wave Trains | p. 183 |
| Chaotic Wave Trains | p. 185 |
| Rotating Spiral Waves | p. 188 |
| Advective Limit for a Rotating Spiral | p. 188 |
| Propagating Finger | p. 191 |
| Slender Spiral Band | p. 195 |
| Tip Meandering | p. 197 |
| Phenomenology of Complex Spiral Motion | p. 200 |
| Scroll Waves | p. 204 |
| Amplitude Equations for Patterns | p. 209 |
| Spatially Modulated Patterns | p. 209 |
| Ginzburg-Landau Equation | p. 209 |
| Newell-Whitehead-Segel Equation | p. 211 |
| Variational Formulation | p. 212 |
| Stationary Solutions | p. 213 |
| Stability of Stationary Solutions | p. 216 |
| Phase Dynamics | p. 218 |
| Universal Form of Phase Equations | p. 218 |
| Variational Formulation | p. 219 |
| Long-Scale Expansion | p. 222 |
| Covariant Phase-Amplitude Equation | p. 223 |
| Defects in Striped Patterns | p. 225 |
| Natural Patterns | p. 225 |
| Phase Field of a Dislocation | p. 227 |
| Dislocations in NWS Equation | p. 229 |
| Dislocation Core | p. 232 |
| Disclinations | p. 234 |
| Domain Walls | p. 235 |
| Motion of Dislocations | p. 238 |
| The Nature of the Driving Force | p. 238 |
| Phase Field of a Moving Defect | p. 239 |
| Dissipation Integral and Peach-Kohler Force | p. 241 |
| Matched Asymptotic Expansions | p. 244 |
| Interaction of Dislocations | p. 247 |
| Motion in a Supercriticality Ramp | p. 252 |
| Propagation of Pattern and Pinning | p. 254 |
| Wavelength Selection in a Propagating Pattern | p. 254 |
| Self-Induced Pinning | p. 257 |
| Geometry of Pinned States | p. 260 |
| Crystallization Kinetics | p. 263 |
| Pinning of Defects | p. 267 |
| Hexagonal Patterns | p. 271 |
| Triplet Amplitude Equations | p. 271 |
| Skewed Triplets | p. 273 |
| Penta-Hepta Defects | p. 275 |
| Domain Boundaries | p. 279 |
| Propagation of the Hexagonal Pattern | p. 283 |
| Amplitude Equations for Waves | p. 287 |
| Plane Waves | p. 287 |
| Complex Ginzburg-Landau Equation | p. 287 |
| Perturbations of Plane Waves | p. 289 |
| Phase Equations | p. 292 |
| Propagation of Wave Pattern | p. 294 |
| Coupled CGL Equations | p. 295 |
| One-Dimensional Structures | p. 297 |
| Classification of 1D Solutions | p. 297 |
| Holes and Wavenumber Kinks | p. 299 |
| Modulated Waves and Phase Turbulence | p. 302 |
| Transition to Defect Chaos | p. 305 |
| Sources and Sinks in Coupled CGL Equations | p. 307 |
| Spiral Waves | p. 310 |
| Symmetric Spiral | p. 310 |
| Asymptotic Relations | p. 312 |
| Nondissipative Limit | p. 316 |
| Acceleration Instability | p. 318 |
| Interaction of Spiral Vortices | p. 320 |
| Nonradiative Limit | p. 320 |
| Weakly Radiative Vortices | p. 322 |
| Strong Radiation and Shocks | p. 326 |
| Multispiral Patterns | p. 329 |
| Period Doubling in Spirals | p. 333 |
| Line Vortices and Scroll Waves | p. 336 |
| Curvature-Driven Motion | p. 336 |
| Nondissipative Motion | p. 339 |
| Dissipative Nonradiative Line Vortex | p. 343 |
| Instability of Line Vortices | p. 344 |
| Resonant Oscillatory Forcing | p. 347 |
| Broken Phase Symmetry | p. 347 |
| Forcing at Double Frequency | p. 348 |
| Ising and Bloch Fronts | p. 350 |
| Higher Resonances | p. 354 |
| References | p. 357 |
| Index | p. 365 |
| Table of Contents provided by Ingram. All Rights Reserved. |
