Stability for amplitude spiral wave in complex Ginzburg-Landau equation

The study of a novel amplitude spiral wave in complex Ginzburg-Landau equation system is performed. The competition results between amplitude spiral waves and phase spiral waves and spatiotemporal chaos can be divided into four kind of regimes: regimes I and Ⅲ, in which the space of amplitude spiral waves is invaded by phase spiral waves, regime Ⅱ, in which the amplitude spiral waves are stronger than phase spiral waves, and regime IV, in which we have various results due to the existence of spatiotemporal chaos. Analysing the frequencies of amplitude spirals, phase spirals and spatiotemporal chaos, we find that when the parameters of spiral wave system α1=-1.34 and β1=0.35, the spiral wave with higher frequency will have better stability and can invade into low-frequency pattern space. The competition results are influenced by frequency of real part of the system variable. Our frequency analyses accord well with the numerical observations.