The concept of Box Invariance for biologically-inspired dynamical systems
Alessandro Abate, Ashish Tiwari, Shankar Sastry

Citation
Alessandro Abate, Ashish Tiwari, Shankar Sastry. "The concept of Box Invariance for biologically-inspired dynamical systems". Technical report, University of California, Berkeley, UCB/EECS-2006-185, December, 2006.

Abstract
In this paper we introduce a special notion of Invariance Set for certain classes of dynamical systems: the concept has been inspired by our experience with models drawn from Biology. We claim that Box Invariance, that is, the existence of “boxed” invariant regions, is a characteristic of many biologically-inspired dynamical models, especially those derived from stoichiometric reactions. Moreover, box invariance is quite useful for the verification of safety properties of such systems. This paper presents effective characterization of this notion for linear and affine systems, the study of the dynamical properties it subsumes, computational aspects of checking for box invariance, and a comparison with related concepts in the literature. The concept is illustrated using two models from biology.

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Citation formats

• HTML

  Alessandro Abate, Ashish Tiwari, Shankar Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/218.html"
  ><i>The concept of Box Invariance for
  biologically-inspired dynamical systems</i></a>,
  Technical report,  University of California, Berkeley,
  UCB/EECS-2006-185, December, 2006.

• Plain text

  Alessandro Abate, Ashish Tiwari, Shankar Sastry. "The
  concept of Box Invariance for biologically-inspired
  dynamical systems". Technical report,  University of
  California, Berkeley, UCB/EECS-2006-185, December, 2006.

• BibTeX

  @techreport{AbateTiwariSastry06_ConceptOfBoxInvarianceForBiologicallyinspiredDynamical,
      author = {Alessandro Abate and Ashish Tiwari and Shankar
                Sastry},
      title = {The concept of Box Invariance for
                biologically-inspired dynamical systems},
      institution = {University of California, Berkeley},
      number = {UCB/EECS-2006-185},
      month = {December},
      year = {2006},
      abstract = {In this paper we introduce a special notion of
                Invariance Set for certain classes of dynamical
                systems: the concept has been inspired by our
                experience with models drawn from Biology. We
                claim that Box Invariance, that is, the existence
                of �boxed� invariant regions, is a
                characteristic of many biologically-inspired
                dynamical models, especially those derived from
                stoichiometric reactions. Moreover, box invariance
                is quite useful for the verification of safety
                properties of such systems. This paper presents
                effective characterization of this notion for
                linear and affine systems, the study of the
                dynamical properties it subsumes, computational
                aspects of checking for box invariance, and a
                comparison with related concepts in the
                literature. The concept is illustrated using two
                models from biology.},
      URL = {http://chess.eecs.berkeley.edu/pubs/218.html}
  }
  

Posted by Alessandro Abate on 24 Apr 2007.
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