一类新混沌系统的几何分析

摘要

Based on Poincare 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 attractor.%基于PoincaM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.