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Publications about 'Petri nets'
Articles in journal or book chapters
  1. D. Angeli, P. de Leenheer, and E.D. Sontag. Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws. SIAM Journal on Applied Mathematics, 71:128-146, 2011. [PDF] Keyword(s): biochemical networks, fluxes, Petri nets, persistence, biochemical networks with inputs.
    Abstract:
    New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement existing ones. The new results allow the consideration of reaction rates which are time-varying, thus incorporating the effects of external signals, and also relax the assumption of existence of global conservation laws, thus allowing for inflows (production) and outflows (degradation). For time-invariant networks parameter-dependent conditions for persistence of certain classes of networks are provided. As an illustration, two networks arising in the systems biology literature are analyzed, namely a hypoxia and an apoptosis network.


  2. D. Angeli, P. de Leenheer, and E.D. Sontag. Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates. J. Mathematical Biology, 61:581-616, 2010. [PDF] Keyword(s): biochemical networks, fluxes, monotone systems, reaction cordinates, Petri nets, persistence, futile cycles.
    Abstract:
    This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence without making assumptions on the form of the kinetics (e.g., mass-action) of the dynamical equations involved, and relying only on stoichiometric constraints. The key idea is to find an alternative representation under which the resulting system is monotone. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property.


  3. D. Angeli, P. de Leenheer, and E.D. Sontag. Chemical networks with inflows and outflows: A positive linear differential inclusions approach. Biotechnology Progress, 25:632-642, 2009. [PDF] Keyword(s): biochemical networks, fluxes, differential inclusions, positive systems, Petri nets, persistence, switched systems.
    Abstract:
    Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to biochemical reaction networks with inflows and outflows. Included is also a characterization of exponential stability of general homogeneous switched systems


  4. D. Angeli, P. de Leenheer, and E.D. Sontag. A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences, 210:598-618, 2007. 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. [PDF] Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.
    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.


Conference articles
  1. D. Angeli, P. de Leenheer, and E.D. Sontag. On persistence of chemical reaction networks with time-dependent kinetics and no global conservation laws. In Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009, pages 4559-4564, 2009. [PDF] Keyword(s): biochemical networks, fluxes, Petri nets, persistence, biochemical networks with inputs.
    Abstract:
    This is a very summarized version ofthe first part of the paper "Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws".


  2. D. Angeli, P. de Leenheer, and E.D. Sontag. Petri nets tools for the analysis of persistence in chemical networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007, 2007. Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.



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Last modified: Thu Nov 23 10:40:57 2017
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