Towards a qualitative theory of differential automata. 2. An analog of the Poincare-Bendixon theorem

The paper considers an important class of hybrid dynamical systems called differential automata. For planar differential automata, we derive an analog of the classic Poincare-Bendixon theorem. This result is applied to demonstrate that, for the so-called three buffer switched arrival system, certain control policies exhibit not chaotic but simple periodic dynamics.