基于坐标旋转变换意义下的三维全局耦合离散混沌系统对称与隐藏动力学的识别与分析  

Recognition and analysis of symmetric dynamics and hidden dynamics of a three-dimensional global coupling discrete chaotic system based on the coordinate rotation transformation

作　　者：姚潇悦 李险峰[1] 江俊[2] 梁以德[3] 王淑英 YAO Xiao-Yue;LI Xian-Feng;JIANG Jun;LIANG Yi-De;WANG Shu-Ying(School of Mathematics and Physics,Lanzhou Jiao tong University,Lanzhou 730070,China;State Key Laboratory for Strength and Vibration,Xi?an Jiaotong University,Xi'an 710049,China;・Department of Civil and Architectural Engineering,City University of HongKong,HongKong 999077,China)

机构地区：[1]兰州交通大学数理学院,兰州730070 [2]西安交通大学机械结构强度与振动国家重点实验室,西安710049 [3]香港城市大学建筑与土木工程学系,中国香港999077

出　　处：《四川大学学报（自然科学版）》2022年第4期108-114,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11962011,11772243);甘肃省自然科学基金(20JR10RA223)。

摘　　要：本文用一维Logistic映射代替平均场,全局耦合构造了一类三维混沌映射,并利用坐标旋转变换对耦合系统的复杂动力学和隐藏动力学分析和识别.通过展示耦合系统的吸引子、分岔图及共存吸引域在坐标旋转前后的对比,我们发现原耦合系统经由坐标旋转后,其吸引子及其共存吸引域在旋转平面上的投影均具有很好的三角对称性.此外,我们在双参数稳态分布图上增加了余维1与余维2分岔线,提供了一种在参数平面域内发现可能存在的吸引子共存的方法.双参数稳态分布虽然与坐标旋转变换无关,但其正交变换的特性可大幅提高运算效率.A three-dimensional chaotic map is created with global coupling by replacing the mean field with standard 1-D Logistic map. The complex dynamics and hidden dynamics of the coupled system are analyzed and identified by coordinate rotation transformation. The attractors and the bifurcation structure together with the coexisting attraction domain of the coupled system, are shown in respective diagram before and after utilizing the coordinate rotation transformation. The comparison among them shows that the projection of the attractors and the coexisting basin of attraction of the original coupled system on the rotated plane are of triangular symmetry. Co-dimension 1 and 2 bifurcation lines are superimposed on the two-parameter steady-state diagrams. It provides a way to recognize possible coexisting attractors in parameter domains. Both two-parameter steady state distribution diagram and bifurcation lines are independent of coordinate rotation transformation. However, their computation speed would be greatly accelerated with the help of orthogonal transformation.

关 键 词：混沌映射 坐标旋转变换 三角对称性 识别 投影 

分 类 号：O415.5[理学—理论物理]