Superspiral structures of meandering and drifting spiral waves.

The spatiotemporal superstructure of meandering and drifting spiral waves is explained analytically. It is also demonstrated that the Hopf eigenmode that causes the transition to meandering waves is weakly exponentially localized at onset but grows exponentially slightly before onset.

[1]  W. Skaggs,et al.  Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable oregonator model , 1989 .

[2]  D. Barkley,et al.  Euclidean symmetry and the dynamics of rotating spiral waves. , 1994, Physical review letters.

[3]  Barkley,et al.  Linear stability analysis of rotating spiral waves in excitable media. , 1992, Physical review letters.

[4]  Zhou,et al.  Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system , 2000, Physical review letters.

[5]  M. Eiswirth,et al.  Turbulence due to spiral breakup in a continuous excitable medium. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Weber,et al.  Stability limits of spirals and traveling waves in nonequilibrium media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[7]  Petrov,et al.  Transition from Simple Rotating Chemical Spirals to Meandering and Traveling Spirals. , 1996, Physical review letters.

[8]  H. Engel,et al.  Chemical Waves and Patterns , 1996 .

[9]  A. Winfree.  When time breaks down , 1987 .

[10]  Harm Hinrich Rotermund,et al.  Reaction diffusion patterns in the catalytic CO‐oxidation on Pt(110): Front propagation and spiral waves , 1993 .

[11]  V. I. Krinsky,et al.  Super-spiral structures in an excitable medium , 1991, Nature.

[12]  Scheel,et al.  Absolute versus convective instability of spiral waves , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  B. Hess,et al.  Spiral wave dynamics as a function of proton concentration in the ferroin-catalyzed Belousov-Zhabotinskii reaction , 1990 .

[14]  Björn Sandstede,et al.  Dynamics of Spiral Waves on Unbounded Domains Using Center-Manifold Reductions , 1997 .

[15]  Martin Golubitsky,et al.  Meandering of the Spiral Tip: An Alternative Approach , 1997 .