Journal of Mathematical Chemistry

, Volume 49, Issue 6, pp 1163–1179 | Cite as

Finding complex balanced and detailed balanced realizations of chemical reaction networks

  • Gábor Szederkényi
  • Katalin M. Hangos
Original Paper


Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not “encoded” in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.


Reaction kinetic systems Mass action kinetics Linear programming 

Mathematics Subject Classification (2000)

80A30 chemical kinetics 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Process Control Research Group, Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Electrical Engineering and Information SystemsUniversity of PannoniaVeszprémHungary

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