# A Poincaré–Bendixson theorem for hybrid dynamical systems on directed graphs

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## Abstract

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.

## Keywords

Poincaré–Bendixson theorem Hybrid systems Periodic orbits Directed graphs## Mathematics Subject Classification

37E25 37C27 34A38 37C10 34A34## Notes

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