Rayleigh-Bénard convection with rotation at small Prandtl numbers.- Chaotic intermittency of patterns in symmetric systems.- Heteroclinic cycles and phase turbulence.- Hopf bifurcation in anisotropic systems.- Heteroclinic cycles in symmetrically coupled systems.- Symmetry and pattern formation in coupled cell networks.- Spatial hidden symmetries in pattern formation.- Stability boundaries of the dynamic states in pulsating and cellular flames.- A quantitative description of the relaxation of textured patterns.- Forced symmetry breaking: theory and applications.- Spatiotemporal patterns in electrochemical systems.- Memory effects and complex patterns in a catalytic surface reaction.- Bursting mechanisms for hydrodynamical systems.- Bifurcation from periodic solutions with spatiotemporal symmetry.- Resonant pattern formation in a spatially extended chemical system.- Time-dependent pattern formation for two-layer convection.- Localized structures in pattern-forming systems.- Pattern formation in a surface reaction with global coupling.- Dynamical behavior of patterns with Euclidean symmetry.- Pattern selection in a diffusion-reaction system with global or long-range interaction.- Dynamics of kinks and vortices in Josephson-junction arrays.- Josephson junction arrays: Puzzles and prospects.- List of Participants.
This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE Pattern formation has been studied intensively for most of this cen tury by both experimentalists and theoreticians, and there have been many workshops and conferences devoted to the subject. In the IMA workshop on Pattern Formation in Continuous and Coupled Systems held May 11-15, 1998 we attempted to focus on new directions in the patterns literature.
This volume contains a number of mini-review articles authored by speakers and attendees at the IMA workshop on Pattern Formation in Continuous and Coupled Systems. Pattern formation has been studied intensively for most of this century by both experimentalists and theoreticians. This workshop focused on new directions in the patterns literature. Systems that generate new types of pattern such as discrete coupled systems, systems with global coupling, and combustion experiments were stressed, as were new types of pattern. The mini-reviews in this volume are intended to be pointers to the current literature for researchers at all levels and to have extensive bibliographies. They are also intended to discuss why certain