吸引子
奇点
吸引力
数学
边界(拓扑)
分形
不变(物理)
多项式的
指数稳定性
平衡点
数学分析
弹道
曲线的奇点
物理
非线性系统
量子力学
微分方程
天文
哲学
语言学
数学物理
作者
Weijian Huang,Yuhong Zhang,Xiao‐Song Yang
标识
DOI:10.1142/s0218127422502352
摘要
Even if a system has only one stable equilibrium point, its dynamics can still be complicated. In the case of the equilibrium point with a complicated boundary of the attraction basin, it is probably difficult to predict the long-term behavior of the trajectory starting from a point outside but near the boundary. The exploration of such systems is helpful for deepening our understanding of the dynamics of complex systems. This paper studies a class of three-dimensional polynomial systems with a nonelementary singularity. With parameters satisfying some conditions, the asymptotic stability of the origin is proved and the complexity of the attraction basin is investigated. It is demonstrated that the boundary of the attraction basin of the origin has a fractal structure in the following sense: An invariant set homeomorphic to the well-known Lorenz strange attractor is contained in the basin boundary. Based on the non-negative function we constructed, how fast a trajectory of the system tends to the asymptotically stable nonelementary singularity is measured.
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