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

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.

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

A three-dimensional chaotic map is created with global coupling by substituting the mean field with standard 1-D Logistic map. The complex dynamics and hidden dynamics of coupled system are analyzed and identified by coordinate rotation transformation. The attractors and the bifurcation structure together with the coexistent 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.