Box invariance for biologically-inspired dynamical systems

In this paper, motivated in particular by models drawn from biology, we introduce the notion of box invariant dynamical systems. We argue that box invariance, that is, the existence of a box-shaped positively invariant region, is a characteristic of many biologically-inspired dynamical models. Box invariance is also useful for the verification of stability and safety properties of such systems. This paper presents effective characterization of this notion for some classes of systems, computational results on checking box invariance, the study of the dynamical properties it subsumes, and a comparison with related concepts in the literature. The concept is illustrated using models derived from different case studies in biology.