环域反馈下复Ginzburg-Landau系统的螺旋波动力学行为  

Dynamics of Spiral Waves in Complex Ginzburg-Landau Systems Subjected to Feedback Derived from an Annular Domain

作　　者：陈绍英 王雪丽 高志梅 袁国勇[2] CHEN Shaoying;WANG Xueli;GAO Zhimei;YUAN Guoyong(Journal Editorial Department,Hulunbeier College,Hulunbeier,Inner Mongolia 021008,China;College of Physics,Hebei Normal University,Shijiazhuang,Hebei 050024,China)

机构地区：[1]呼伦贝尔学院学报编辑部,内蒙古呼伦贝尔021008 [2]河北师范大学物理学院,河北石家庄050024

出　　处：《计算物理》2022年第1期118-126,共9页Chinese Journal of Computational Physics

基　　金：内蒙古自治区高等学校科学研究重点项目(NJZZ14310);河北省自然科学基金项目(A2020205010);河北省高等学校科学技术研究项目(ZD2020186)资助。

摘　　要：针对自激振荡系统的复金兹伯格-朗道(Complex Ginzbury-Landau,简称CGL)方程,研究圆形环域与方形环域两种反馈控制下的螺旋波动力学。结果表明:圆形环域反馈控制下,螺旋波波头通常经过一段过渡漂移后进入圆形吸引子,圆形吸引子的半径以及反馈刚启动时波头的漂移方向随环域参数呈周期性变化,过渡漂移阶段波头轨道的平缓程度与复反馈信号模的时间函数中钟形部分的陡度有关,且反馈增益的正负与大小也会影响受控螺旋波的动力学行为。方形环域反馈控制下的螺旋波波头的吸引子更为丰富,主要包括方形吸引子、小的极限环吸引子、菱形吸引子以及点吸引子,点吸引子通常位于方形环域的两条对角线上,且波头运动随环域控制参数呈现规律性变换。We studied dynamics of spiral waves subjected to a feedback control, where the feedback signal is obtained with integral in an annular region. As the annular region is circular, the spiral tip usually enters a circular attractor after a transient drift, and radius of the attractor varies periodically with parameters of the annular region. With the change of these parameters, drift direction of the spiral tip at the beginning of feedback also has a periodic change. In the phase of transient drift, modulus function of the complex feedback signal is bell-shaped, and the steepness of the bell is related to the smoothness of the drift trajectory. The sign and value of the feedback gain affect the dynamical behavior of the controlled spiral. As the annular region is square, final attractors of the spiral tip are more abundant, including mainly square attractor, limit circle attractor with small amplitude, diamond attractor and point attractor, where the point attractors are usually on the diagonal lines of the square. Here, trajectory of the spiral tip has a regular change with control parameters of the annual region as well.

关 键 词：螺旋波 Ginzburg-Landau系统 反馈控制 吸引子 

分 类 号：O415[理学—理论物理]