Pattern Formation in Continuous and Coupled Systems

1. Front Matter

   Pages i-xvi

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2. Rayleigh-Bénard Convection with Rotation at Small Prandtl Numbers

   • Guenter Ahlers, Kapil M.S. Bajaj

   Pages 1-9

3. Chaotic Intermittency of Patterns in Symmetric Systems

   • Peter Ashwin

   Pages 11-24

4. Heteroclinic Cycles and Phase Turbulence

   • F.H. Busse, R.M. Clever

   Pages 25-32

5. Hopf Bifurcation in Anisotropic Systems

   • Gerhard Dangelmayr, Michael Wegelin

   Pages 33-47

6. Heteroclinic Cycles in Symmetrically Coupled Systems

   • Michael Field

   Pages 49-64

7. Symmetry and Pattern Formation in Coupled Cell Networks

   • Martin Golubitsky, Ian Stewart

   Pages 65-82

8. Spatial Hidden Symmetries in Pattern Formation

   • M. Gabriela M. Gomes, Isabel S. Labouriau, Eliana M. Pinho

   Pages 83-99

9. Stability Boundaries of the Dynamic States in Pulsating and Cellular Flames

   • Michael Gorman

   Pages 101-110

10. A Quantitative Description of the Relaxation of Textured Patterns

    • Gemunu H. Gunaratne

    Pages 111-119

11. Forced Symmetry Breaking: Theory and Applications

    • Frederic Guyard, Reiner Lauterbach

    Pages 121-135

12. Spatiotemporal Patterns in Electrochemical Systems

    • J. L. Hudson

    Pages 137-146

13. Memory Effects and Complex Patterns in a Catalytic Surface Reaction

    • R. Imbihl

    Pages 147-156

14. Bursting Mechanisms for Hydrodynamical Systems

    • E. Knobloch, J. Moehlis

    Pages 157-174

15. Bifurcation From Periodic Solutions with Spatiotemporal Symmetry

    • Jeroen S. W. Lamb, Ian Melbourne

    Pages 175-191

16. Resonant Pattern Formation in a Spatially Extended Chemical System

    • Anna L. Lin, Valery Petrov, Harry L. Swinney, Alexandre Ardelea, Graham F. Carey

    Pages 193-201

17. Time-Dependent Pattern Formation for Two-Layer Convection

    • Y. Renardy, C. G. Stoltz

    Pages 203-213

18. Localized Structures In Pattern-Forming Systems

    • Hermann Riecke

    Pages 215-229

19. Pattern Formation in a Surface Reaction with Global Coupling

    • Harm Hinrich Rotermund

    Pages 231-247

20. Dynamical Behavior of Patterns with Euclidean Symmetry

    • BjöRn Sandstede, Arnd Scheel, Claudia Wulff

    Pages 249-264

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.

• bifurcation
• differential equation
• dynamical systems
• ordinary differential equation
• stability
• turbulence

• Department of Mathematics, University of Houston, Houston, USA

  Martin Golubitsky

• Department of Chemical Engineering, University of Houston, Houston, USA

  Dan Luss

• Theoretical and Applied Mechanics, Cornell University, Ithaca, USA

  Steven H. Strogatz

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