一个二维冲击振子模型的相平面结构

PHASE PLANE OF A 2-D IMPACT OSCILLATOR MODEL

讨论了二维冲击振子模型的相平面结构 ,解析得到混沌吸引子吸引域边界上鞍点的稳定和不稳定流形的表示式 ,并说明了混沌吸引子就是此不稳定流形的闭包 。

This paper discusses a model of a 2 d impact oscillator. The expressions of the stable and unstable manifolds of a saddle node, which is on the boundary of the basin of a chaotic attractor, is analytically solved, and shown that the chaotic attractor is the closure of the unstable manifold, and its basin is the closure of the stable manifold.