一类新混沌系统的几何分析  

Geometric Analysis of a Class of the New Chaotic System

作　　者：黄燮桢 刘永建[2] 黄秋健 Xiezhen Huang;Yongjian Liu;Qiujian Huang(School of Mathematics and Statistics, Minnan Normal University, Fujian Zhangzhou 363000;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Guangxi Yulin 537000;School of Science, Guangxi University for Nationalities, Nanning 530006)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]玉林师范学院广西高校复杂系统优化与大数据处理重点实验室,广西玉林537000 [3]广西民族大学理学院,南宁530006

出　　处：《数学物理学报（A辑）》2019年第2期339-347,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561069);广西自然科学基金(2016GXNSFBA380170;2017GXNSFAA198234);福建省数学类研究生教育创新基地项目(1013-313009);广西高等学校高水平创新团队及卓越学者计划项目(文件编号[2018]35)~~

摘　　要：基于Poincare紧致化技术,分析一类三维混沌系统的全局动力学行为.研究表明系统在无穷远处的奇点高度退化且不稳定.该文也通过设计一个不改变系统奇点结构的线性控制器,构造了一个受控系统,研究发现受控系统在特定参数组条件下,存在一簇退化奇异异宿轨.结合数值仿真结果,论文指出,当参数b和c发生微小扰动时,受控系统异宿环破裂,产生新的混沌吸引子.希冀这些研究对解释系统混沌几何机理能提供有益帮助。Based on Poincaré compactification technology, the global dynamics behavior of three dimensional chaotic system is studied. The results show that the equilibria at infinity are unstable and highly degraded. The controlled system with a linear controller which does not change the singularity structure has a bunch of degenerate singular orbits. The chaotic attractors for the system in the case of small parameters b and c are found numerically, and thus the nearby singularly degenerate heteroclinic cycles. It is hoped that the investigation of this paper will be quite beneficial for further studies of the geometrical structure for the chaotic attractor.

关 键 词：Poincaré紧致化 无穷远奇点 奇异退化异宿轨 混沌系统 

分 类 号：O175[理学—数学]