Spiral and antispiral waves are studied numerically in two examples ofoscillatory reaction-diffusion media and analytically in the correspondingcomplex Ginzburg-Landau equation (CGLE). We argue that both these structuresare sources of waves in oscillatory media, which are distinguished only by thesign of the phase velocity of the emitted waves. Using known analytical resultsin the CGLE, we obtain a criterion for the CGLE coefficients that predictswhether antispirals or spirals will occur in the correspondingreaction-diffusion systems. We apply this criterion to the FitzHugh-Nagumo andBrusselator models by deriving the CGLE near the Hopf bifurcations of therespective equations. Numerical simulations of the full reaction-diffusionequations confirm the validity of our simple criterion near the onset ofoscillations. They also reveal that antispirals often occur near the onset andturn into spirals further away from it. The transition from antispirals tospirals is characterized by a divergence in the wavelength. A tentativeinterpretaion of recent experimental observations of antispiral waves in theBelousov-Zhabotinsky reaction in a microemulsion is given.
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