摘要
为了对多参非解析对称复映射进行动力系统图形化研究,本文研究了含有5个实参非解析4旋转对称复映射■的广义M集的构造以及其非线性迭代函数系的构造等问题.固定5参数空间中的3个参数α,β与γ的取值,构造参数λ与ω组成的参数断面C;用无约束最优化求解方法中的"步长加速法",求解使参数断面C的参数c=(λ,ω)下的迭代映射f_c(z)的Jacobin矩阵为0的局部极值点;计算每个局部极值点的Lyapunov(L)指数,考察局部极值点的轨道特性,将参数断面C划分成逃逸、混沌、吸引和混合参数区域,构造出参数断面C上的广义M集.实现了采用不同参数区域的参数构造动力平面上的混沌吸引子和充满Julia集;在吸引参数区域,根据参数点c下1个迭代映射具有多条吸引周期轨道特性,提出构造非线性迭代函数系方法,生成相应分形.结果表明:采用本文提出的构造广义M集的方法,可以有效进行多参非解析对称映射的动力系统图形化研究,可以大量构造迭代映射族在动力平面上的混沌吸引子、充满Julia集和NIFS的分形.
To research on how visualization of dynamical systems of nonanalytic symmetric complex mappings with multiparameter,we investigate the constructions of the Mset and the NIFS of the mapping of■.Fixing the values of the 3 parametersα,βandγ,set up the cross-section C composed of the parametersλandωin the 5 parameter space.The accelerated direct search algorithmis is used to get the local critical points,which make the the determinant of the Jacobin matrix of the mapping f_c(z)with parameter c=(λ,ω)in the C plane equal 0.Compute the Lyapunov exponential value(L)of the every local critical points.The C plane is divided into the escape region,the chaotic region,the attracting region and the mixed region by the orbital characteristics of the critical points,and the general Mset is constructed in the C plane.The chaotic attractors and the filled-in Julia sets are constructed by choosing the parameters from the different parameter regions of the Mset.For the attracting parameter regions,the methods of constructions of NIFSs and their fractals are present according to the multiorbit characteristics of the mapping f_c(z).The results show that the visualization of dynamical systems of nonanalytic symmetric complex mappings with multiparameter can be validly researched by the methods provided in this paper and the great number of the chaotic attractors,the filled-in Julia sets and the fractals of NIFSs can be easily constructed from this kind of the mapping family.
作者
陈宁
张书玮
王凤英
CHEN Ning;ZHANG Shu-wei;WANG Feng-ying(Faculty of Information&Control Engineering,Shenyang Jianzhu University,Shenyang 110168,China)
出处
《小型微型计算机系统》
CSCD
北大核心
2020年第7期1530-1540,共11页
Journal of Chinese Computer Systems
基金
国家自然科学基金项目(612722536)资助。
