Dynamical Systems: Discrete, Continuous and Hybrid

Ethan Akin

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arXiv · 2307.03815

Dynamical Systems: Discrete, Continuous and Hybrid

Ethan Akin

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Abstract

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation extension) as well as hybrid dynamical systems which combine both continuous time and discrete time dynamics. In a unified way we describe the attractor-repeller structure, Conley's chain recurrence relation and the construction of Lyapunov functions for all of these systems.

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Ethan Akin. 2023-07-07. Dynamical Systems: Discrete, Continuous and Hybrid. https://arxiv.org/abs/2307.03815

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