Before revision:  however, many of the insights from recent developments in this area have largely remained folklore and are not elaborated in existing literature. This article contributes an explicit development of modern methods for checking positively invariant sets of ordinary differential equations and describes two possible characterizations of positive invariants: one based on the real induction principle , and a novel alternative based on topological notions .
After revision:  however, many of the real induction principle , and a novel alternative based on topological notions .