Differentially positive systems
For researchers in dynamical systems and control theory, it generalizes Perron-Frobenius theory to a differential framework, but the results are theoretical and incremental over known monotone systems.
The paper introduces differentially positive systems, whose linearization along any trajectory is positive, and shows that this property induces a conal order constraining asymptotic behavior, extending results beyond linear positive and monotone systems.
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to show that the property induces a (conal) order that strongly constrains the asymptotic behavior of solutions. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space.