@ARTICLE{persistencePetri,
   AUTHOR       = {D. Angeli and de Leenheer, P. and E.D. Sontag},
   JOURNAL      = {Mathematical Biosciences},
   TITLE        = {A Petri net approach to the study of persistence in 
      chemical reaction networks},
   YEAR         = {2007},
   OPTMONTH     = {},
   NOTE         = {Please look at the paper ``A Petri net approach to persistence analysis in chemical reaction networks'' for additional results, not included in the journal paper due to lack of space. See also the preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006},
   OPTNUMBER    = {},
   PAGES        = {598-618},
   VOLUME       = {210},
   KEYWORDS     = {Petri nets, systems biology, biochemical networks, 
      nonlinear stability, dynamical systems, futile cycles},
   PDF          = {../../FTPDIR/angeli_leenheer_sontag_math_biosciences_MBS-D-06-00188R1.pdf},
   ABSTRACT     = { Persistency is the property, for differential equations 
      in Rn, that solutions starting in the positive orthant do not 
      approach the boundary. For chemical reactions and population models, 
      this translates into the non-extinction property: provided that every 
      species is present at the start of the reaction, no species will tend 
      to be eliminated in the course of the reaction. This paper provides 
      checkable conditions for persistence of chemical species in reaction 
      networks, using concepts and tools from Petri net theory, and 
      verifies these conditions on various systems which arise in the 
      modeling of cell signaling pathways. }
}

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