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Pattern Formation in Continuous and Coupled Systems : A Survey Volume - Martin Golubitsky

Pattern Formation in Continuous and Coupled Systems

A Survey Volume

By: Martin Golubitsky (Editor), Dan Luss (Editor), Steven H. Strogatz (Editor)


Published: 22nd June 1999
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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.

Dedication to John David Crawford 1954-1998
Rayleigh-Benard convection with rotation at small Prandtl numbersp. 1
Chaotic intermittency of patterns in symmetric systemsp. 11
Heteroclinic cycles and phase turbulencep. 25
Hopf bifurcation in anisotropic systemsp. 33
Heteroclinic cycles in symmetrically coupled systemsp. 49
Symmetry and pattern formation in coupled cell networksp. 65
Spatial hidden symmetries in pattern formationp. 83
Stability boundaries of the dynamic states in pulsating and cellular flamesp. 101
A quantitative description of the relaxation of textured patternsp. 111
Forced symmetry breaking: theory and applicationsp. 121
Spatiotemporal patterns in electrochemical systemsp. 137
Memory effects and complex patterns in a catalytic surface reactionp. 147
Bursting mechanisms for hydrodynamical systemsp. 157
Bifurcation from periodic solutions with spatiotemporal symmetryp. 175
Resonant pattern formation in a spatially extended chemical systemp. 193
Time-dependent pattern formation for two-layer convectionp. 203
Localized structures in pattern-forming systemsp. 215
Pattern formation in a surface reaction with global couplingp. 231
Dynamical behavior of patterns with Euclidean symmetryp. 249
Pattern selection in a diffusion-reaction system with global or long-range interactionp. 265
Dynamics of kinks and vortices in Josephson-junction arraysp. 283
Josephson junction arrays: Puzzles and prospectsp. 303
List of Participantsp. 311
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387988740
ISBN-10: 0387988742
Series: The IMA Volumes in Mathematics and its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 323
Published: 22nd June 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.47