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Routes to Multiple Equilibria for Mass-Action Kinetic Systems

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  • Antonio A. Alonso
  • Irene Otero-Muras
  • Manuel Pájaro

Abstract

In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. The contribution is twofold. We provide an explicit representation of the set of all positive equilibria attained by the system class in terms of a set of (positive parameter dependent) algebraic relations. With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. Interestingly, some kinetic networks within this latter class are capable of sustaining multiple equilibria for any reaction simplex, as we illustrate with one example.

Suggested Citation

  • Antonio A. Alonso & Irene Otero-Muras & Manuel Pájaro, 2018. "Routes to Multiple Equilibria for Mass-Action Kinetic Systems," Complexity, Hindawi, vol. 2018, pages 1-13, December.
    • Handle: RePEc:hin:complx:3912627
    DOI: 10.1155/2018/3912627
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    References listed on IDEAS

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    1. Irene Otero-Muras & Pencho Yordanov & Joerg Stelling, 2017. "Chemical Reaction Network Theory elucidates sources of multistability in interferon signaling," PLOS Computational Biology, Public Library of Science, vol. 13(4), pages 1-28, April.
    2. Irene Otero-Muras & Julio R Banga & Antonio A Alonso, 2012. "Characterizing Multistationarity Regimes in Biochemical Reaction Networks," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-12, July.
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