Renormalized phase dynamics in oscillatory media

Based on the complex Ginzburg-Landau equation (CGLE), a new mapping model of oscillatory media is proposed. The present dynamics is fully determined by an effective phase field renormalized by amplitude. The model exhibits phase turbulence, amplitude turbulence, and a frozen state reported in the CGLE. In addition, we find a state in which the phase and amplitude have spiral structures with opposite rotational directions. This state is found to be observed also in the CGLE. Thus, one concludes that the behaviors observed in the CGLE can be described by only the phase dynamics appropriately constructed.