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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:  February 29, 2008
Revised:  March 31, 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 92C40, 92C05; Secondary: 82C31, 92B05.

    Citation:
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