Differential Positivity on Compact Sets
For control theorists and dynamical systems researchers, it simplifies the application of differential positivity by focusing on compact sets, but the contribution is incremental.
The paper studies differentially positive systems and provides geometric conditions for differential positivity on compact forward invariant sets, enabling characterization of bistable and periodic behaviors.
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.