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arXiv · 1407.6986

Limit and Morse Sets for Deterministic Hybrid Systems

Kimberly Ayers·Xavier Garcia·Jennifer Kunze·Thomas Rudelius·Anthony Sanchez·Sijing Shao·Emily Speranza
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Abstract

The term "hybrid system" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows one to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition. Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories in a hybrid system with small perturbations behave similarly to those of the unperturbed dynamical system.

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Kimberly Ayers, Xavier Garcia, Jennifer Kunze, Thomas Rudelius, Anthony Sanchez, Sijing Shao, Emily Speranza. 2014-07-25. Limit and Morse Sets for Deterministic Hybrid Systems. https://doi.org/10.1007/s12346-012-0092-y

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