Pattern Formation in Continuous and Coupled Systems

by Golubitsky, Martin; Luss, Dan; Strogatz, Steven H.

• ISBN13: 9780387988740
• ISBN10: 0387988742
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Springer Verlag

Summary

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. The goals were to continue communication between these groups, and to familiarize a larger audience with some of the newer directions in the field. 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 therefore include extensive bibliographies. They are also intended to discuss why certain subjects are currently exciting and worthy of additional research.

Table of Contents

Foreword	v
Preface	vii
Dedication to John David Crawford 1954--1998	ix
Edgar Knobloch
Rayleigh-Benard convection with rotation at small Prandtl numbers	1	(10)
Guenter Ahlers
Kapil M.S. Bajaj
Chaotic intermittency of patterns in symmetric systems	11	(14)
Peter Ashwin
Heteroclinic cycles and phase turbulence	25	(8)
F.H. Busse
R.M. Clever
Hopf bifurcation in anisotropic systems	33	(16)
Gerhard Dangelmayr
Michael Wegelin
Heteroclinic cycles in symmetrically coupled systems	49	(16)
Michael Field
Symmetry and pattern formation in coupled cell networks	65	(18)
Martin Golubitsky
Ian Stewart
Spatial hidden symmetries in pattern formation	83	(18)
M. Gabriela M. Gomes
Isabel S. Labouriau
Eliana M. Pinho
Stability boundaries of the dynamic states in pulsating and cellular flames	101	(10)
Michael Gorman
A quantitative description of the relaxation of textured patterns	111	(10)
Gemunu H. Gunaratne
Forced symmetry breaking: theory and applications	121	(16)
Frederic Guyard
Reiner Lauterbach
Spatiotemporal patterns in electrochemical systems	137	(10)
J.L. Hudson
Memory effects and complex patterns in a catalytic surface reaction	147	(10)
R. Imbihl
Bursting mechanisms for hydrodynamical systems	157	(18)
E. Knobloch
J. Moehlis
Bifurcation from periodic solutions with spatiotemporal symmetry	175	(18)
Jeroen S.W. Lamb
Ian Melbourne
Resonant pattern formation in a spatially extended chemical system	193	(10)
Anna L. Lin
Valery Petrov
Harry L. Swinney
Alexandre Ardelea
Graham F. Carey
Time-dependent pattern formation for two-layer convection	203	(12)
Y. Renardy
C.G. Stoltz
Localized structures in pattern-forming systems	215	(16)
Hermann Riecke
Pattern formation in a surface reaction with global coupling	231	(18)
Harm Hinrich Rotermund
Dynamical behavior of patterns with Euclidean symmetry	249	(16)
Bjorn Sandstede
Arnd Scheel
Claudia Wulff
Pattern selection in a diffusion-reaction system with global or long-range interaction	265	(18)
Moshe Sheintuch
Olga Nekhamkina
Dynamics of kinks and vortices in Josephson-junction arrays	283	(20)
H.S.J. van der Zant
Shinya Watanabe
Josephson junction arrays: Puzzles and prospects	303	(8)
Kurt Wiesenfeld
List of Participants	311