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Networks and Heterogeneous Media

2009, Volume 4, Issue 3: 501-526. doi: 10.3934/nhm.2009.4.501
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Boltzmann maps for networks of chemical reactions and the multi-stability problem

  • 1.
    Institute for Cancer Research and Treatment (IRCC), Str Prov 142, Km 3.95, 10060 Candiolo (Torino)
  • 2.
    Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
  • Received: 01 March 2008 Revised: 01 April 2009

  • Primary: 92C40, 92C05; Secondary: 82C31, 92B05.

  • Boltzmann Maps are a class of discrete dynamical systems that may be used in the study of complex chemical reaction processes. In this paper they are generalized to open systems allowing the description of non-stoichiometrically balanced reactions with unequal reaction rates. We show that they can be widely used to describe the relevant dynamics, leading to interesting insights on the multi-stability problem in networks of chemical reactions. Necessary conditions for multistability are thus identified. Our findings indicate that the dynamics produced by laws like the mass action law, can hardly produce multistable phenomena. In particular, we prove that they cannot do it in a wide range of chemical reactions.

    Citation: Andrea Picco, Lamberto Rondoni. Boltzmann maps for networks of chemical reactions and the multi-stability problem[J]. Networks and Heterogeneous Media, 2009, 4(3): 501-526. doi: 10.3934/nhm.2009.4.501

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  • Boltzmann Maps are a class of discrete dynamical systems that may be used in the study of complex chemical reaction processes. In this paper they are generalized to open systems allowing the description of non-stoichiometrically balanced reactions with unequal reaction rates. We show that they can be widely used to describe the relevant dynamics, leading to interesting insights on the multi-stability problem in networks of chemical reactions. Necessary conditions for multistability are thus identified. Our findings indicate that the dynamics produced by laws like the mass action law, can hardly produce multistable phenomena. In particular, we prove that they cannot do it in a wide range of chemical reactions.


  • This article has been cited by:

    1. Luca Mesin, Flavio Canavero, Lamberto Rondoni, Reduction of Protein Networks Models by Passivity Preserving Projection, 2013, 60, 0253-6102, 247, 10.1088/0253-6102/60/2/18
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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