复Ginzburg-Landau方程中模螺旋波的稳定性研究  

Stability for amplitude spiral wave in complex Ginzburg-Landau equation

作　　者：高继华[1] 王宇[1] 张超[1] 杨海朋[1] 戈早川[1] 

机构地区：[1]深圳大学材料学院,深圳市特种功能材料重点实验室,深圳518060

出　　处：《物理学报》2014年第2期43-50,共8页Acta Physica Sinica

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.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.

关 键 词：螺旋波 复GINZBURG-LANDAU方程 模螺旋波 

分 类 号：O175.13[理学—数学]