  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.
