摘要:
研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域：在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.
Abstract:
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.
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