The purpose of this work is to obtain restrictions on the asymptotic structure of two-dimensional hybrid dynamical systems. Previous results have been achieved by the authors concerning hybrid dynamical systems with a single impact surface and a single state space. Here, this work is extended to hybrid dynamical systems defined on a directed graph; each vertex corresponds to a state space and each directed edge corresponds to an impact.

中文翻译：

---

有向图上混合动力系统的Poincaré–Bendixson定理

这项工作的目的是限制二维混合动力系统的渐近结构。作者已经获得了有关具有单个撞击面和单个状态空间的混合动力系统的先前结果。在这里，这项工作扩展到在有向图上定义的混合动力系统。每个顶点对应一个状态空间，每个有向边对应一个碰撞。