Regensburg 2002 – scientific programme
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DY: Dynamik und Statistische Physik
DY 41: Nichtlineare Dynamik I
DY 41.6: Talk
Thursday, March 14, 2002, 11:15–11:30, H3
Antispirals in extended oscillatory media — •Markus Bär and Lutz Brusch — MPI für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden
Rotating spirals that emit periodic waves are frequently observed in pattern forming reaction-diffusion systems. Recently, inwardly rotating spirals (,,antispirals”) have been observed in the Belousov-Zhabotinsky reaction in a water-in-oil microemulsion (V. K. Vanag and I. R. Epstein, Science 294, 835 (2001)). Using the complex Ginzburg-Landau equation (CGLE) ∂t A = A + (1+i c1) Δ A − (1−ic3)|A|2 A as an approximation for the original reaction-diffusion equations (RDE) near a supercritical Hopf bifurcation, we show that antispirals exist in a wide range of parameters and are related by a symmetry transformation in the c1−c3 plane to the usual outwardly rotating spirals. Relating the CGLE to the original RDE and combining CGLE analytical results on plane waves in the and Hagan’s 1982 result on the selected wavenumber in a spiral, we show that antispirals appear in the RDE for c1 + c3 > 0 with a frequency lower than the bulk frequency of the homogeneous oscillations in the RDE in line with the experimental observations. Illustrations by numerical simulations are provided.