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Summary: Box Invariance for biologically-inspired dynamical systems
Alessandro Abate Ashish Tiwari Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California, at Berkeley {aabate,sastry}@eecs.berkeley.edu
Computer Science Laboratory, SRI International
Menlo Park, CA tiwari@csl.sri.com
Abstract-- 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.
I. INTRODUCTION
A positively invariant set is a subset of the state space of a
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