Journal of Mathematical Chemistry

, Volume 50, Issue 1, pp 274–288 | Cite as

A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks

  • Matthew D. JohnstonEmail author
  • David Siegel
  • Gábor Szederkényi
Original Paper


A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.


Chemical kinetics Stability theory Weak reversibility Linear programming Dynamical equivalence 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Matthew D. Johnston
    • 1
    Email author
  • David Siegel
    • 1
  • Gábor Szederkényi
    • 2
    • 3
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.(Bio)Process Engineering GroupIIM-CSIC, Spanish National Research CouncilVigoSpain
  3. 3.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary

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