A Petri net approach to the study of persistence in chemical reaction networks

David Angeli, Patrick De Leenheer, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review

136 Scopus citations


Persistence is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary of the orthant. 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.

Original languageEnglish (US)
Pages (from-to)598-618
Number of pages21
JournalMathematical Biosciences
Issue number2
StatePublished - Dec 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


  • Biochemical networks
  • Enzymatic cycles
  • Nonlinear dynamics
  • Persistence


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