Development of Standing-wave Labyrinthine Patterns *

Experiments on a quasi-two-dimensional Belousov-Zhabotinsky (BZ) reaction-diffusion system, pe- riodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns f orm that consist ofinterpenetrating fingers off requency-locked regions differing in phase by π. Analysis of a forced complex Ginzburg-Landau equation captures both mechanisms observed for the f ormation ofthe labyrinths in the BZ experiments: a transverse instability off ront structures and a nucleation of stripes from unlocked oscillations. The labyrinths are found in the experiments and in the model at a similar location in the forcing amplitude and frequency parameter plane.

[1]  H K Park,et al.  Frequency locking in spatially extended systems. , 2001, Physical review letters.

[2]  G. E. Molau Colloidal and morphological behavior of block and graft copolymers : proceedings of an American Chemical Society symposium held at Chicago, Illinois, September 13-18, 1970 , 2012 .

[3]  Valery Petrov,et al.  Resonant pattern formation in achemical system , 1997, Nature.

[4]  J. Gilli,et al.  Excitability and Defect-Mediated Turbulence in Nematic Liquid Crustal , 1995 .

[5]  E. Meron,et al.  Multiphase patterns in periodically forced oscillatory systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Lee,et al.  Lamellar structures and self-replicating spots in a reaction-diffusion system. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Stéphane Métens,et al.  Pattern selection in bistable systems , 1997 .

[8]  Carey,et al.  Resonant phase patterns in a reaction-diffusion system , 2000, Physical review letters.

[9]  Katharina Krischer,et al.  Spatio-Temporal Pattern Formation , 1999 .

[10]  Kjartan Pierre Emilsson,et al.  Strong resonances of spatially distributed oscillators: a laboratory to study patterns and defects , 1992 .

[11]  De Wit A,et al.  Spatiotemporal dynamics near a codimension-two point. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Price,et al.  Resonant patterns through coupling with a zero mode. , 1995, Physical review letters.

[13]  H. Swinney,et al.  Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.

[14]  Resonance in periodically inhibited reaction-diffusion systems , 2002 .

[15]  Ehud Meron,et al.  Phase Front Instability in Periodically Forced Oscillatory Systems , 1998, patt-sol/9803002.

[16]  Hagberg,et al.  From labyrinthine patterns to spiral turbulence. , 1994, Physical review letters.

[17]  Albert Libchaber,et al.  Quasi-Periodicity and Dynamical Systems: An Experimentalist's View , 1988 .

[18]  Frisch,et al.  Spiral waves in liquid crystal. , 1994, Physical review letters.

[19]  M. Seul,et al.  Domain Shapes and Patterns: The Phenomenology of Modulated Phases , 1995, Science.

[20]  E. Meron,et al.  On the origin of traveling pulses in bistable systems , 1997, patt-sol/9703007.

[21]  Coullet,et al.  Breaking chirality in nonequilibrium systems. , 1990, Physical review letters.

[22]  Sano,et al.  Points, walls, and loops in resonant oscillatory media. , 1995, Physical review letters.

[23]  J. Gambaudo Perturbation of a Hopf Bifurcation by an External Time- Periodic Forcing , 1985 .

[24]  On Mode Interactions in Reaction Diffusion Equation with Nearly Degenerate Bifurcations , 1980 .