耦合复Ginzburg-Landau方程中的相-模螺旋结构相似性

深圳大学材料学院,深圳市特种功能材料重点实验室,广东深圳518060

微分动力系统; 时空系统; 斑图; 复Ginzburg-Landau方程; 单向耦合; 螺旋结构; 模螺旋波

Similarity of spiral structures between phase and amplitude in coupled complex Ginzburg-Landau equation
Gao Jihua, Shi Wenmao, Zhang Chao, Ge Zaochuan, and Yang Haitao

College of Materials Science and Engineering, Key Laboratory of Special Functional Materials of Shenzhen, Shenzhen University, Shenzhen 518060, Guangdong Province, P.R.China

differential dynamic system; spatiotemporal system; pattern; complex Ginzburg-Landau equation; coupled system; spiral structures; amplitude spiral

DOI: 10.3724/SP.J.1249.2016.03272

备注

以二维复Ginzburg-Landau方程为模型,研究单向耦合时空系统中的斑图动力学行为.以稳定的模螺旋波为驱动系统,讨论响应系统在不同耦合强度下的时空斑图动力学行为.通过同步函数与系统相-模频率分析发现,在弱耦合强度条件下,驱动系统的相与响应系统的模会在螺旋结构上出现相似性.分别用靶波与平面波作驱动系统,发现同样现象.研究结果证明,随着耦合强度的增大,单向耦合复Ginzburg-Landau方程系统的耦合行为遵循从非同步、相与模螺旋结构上的相似到完全同步的过程.该现象同时解释了模螺旋波的产生.

We study the dynamic behavior in a unidirectionally coupled system based on a model of the two-dimensional complex Ginzburg-Landau equation. We discuss the spatiotemporal patterns in the response system driven by a stable amplitude spiral wave with different coupling strengths. By analyzing the synchronization function and frequency characteristic in the amplitudes of the drive system and the response system, we observe the similarity of spiral structures between phase and amplitude under weak coupling conditions. The same phenomenon is also observed with the driving signals of target waves and plane waves, respectively. This proves that the process of synchronization in the unidirectional coupled system has three steps: from out of synchronization to similarity of spiral structures between phase and amplitude, and finally to complete synchronization. This phenomenon explains the occurrence of amplitude spirals.

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