Journal of Mathematical Chemistry

, Volume 49, Issue 7, pp 1263–1282

Linear conjugacy of chemical reaction networks

Original Paper

DOI: 10.1007/s10910-011-9817-4

Cite this article as:
Johnston, M.D. & Siegel, D. J Math Chem (2011) 49: 1263. doi:10.1007/s10910-011-9817-4


Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant species. It is known that two networks may possess the same governing mass-action dynamics despite disparate network structure. To date, however, there has only been limited work exploiting this phenomenon even for the cases where one network possesses known dynamics while the other does not. In this paper, we bring these known results into a broader unified theory which we call conjugate chemical reaction network theory. We present a theorem which gives conditions under which two networks with different governing mass-action dynamics may exhibit the same qualitative dynamics and use it to extend the scope of the well-known theory of weakly reversible systems.


Chemical kineticsStability theoryPersistenceComplex balancingDynamical equivalence

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada