TL;DR
This paper explores differential positivity on compact sets, providing geometric conditions and demonstrating its use in characterizing bistable and periodic behaviors in dynamical systems.
Contribution
It introduces geometric conditions for differential positivity on compact sets and simplifies its application in analyzing system behaviors.
Findings
Differential positivity characterizes bistability and periodicity.
Compact sets facilitate the application of differential positivity.
Geometric conditions for differential positivity are established.
Abstract
The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization of bistable and periodic behaviors. Geometric conditions for differential positivity are provided. The introduction of compact sets simplifies the use of differential positivity in applications.
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