Dynamics and Bifurcation of Patterns in Dissipative Systems

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World Scientific, 2004 - Science - 389 pages
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Understanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.
 

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Contents

Symmetry and Pattern Formation on the Visual Cor
3
Matrix Free Approach in the Numerical Analysis
20
Validity of the GinzburgLandau Approximation
39
Stability and Bifurcation from Relative Equilibria
58
Rotating Magnetoconvection with Magnetostrophic Balance
78
Pattern Formation on a Sphere
102
Convergence Properties of Fourier Mode Representa
124
Phase Diffusion and Weak Turbulence Survey Article
143
Heterogeneous Pacemakers in Oscillatory Media
214
A FiniteDimensional Mechanism Responsible
231
Biological Lattice Gas Models
274
A Comparison of Optimal Low Dimensional Projec
292
Linear and Nonlinear Nusselt Number Measure
309
Characterizations of Far from Equilibrium Structures
319
Dynamics near Robust Heteroclinic Cycles
329
Internal Dynamics of Intermittency
357

Pattern Formation and Parametric Resonance
158
Mean Flow Effects in Model Equations for Faraday Waves
174
Rogue Waves and the BenjaminFeir Instability
194
Experiments with Dictyostelium Discoideum Amoe
373
Index
387
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