Realizations of kinetic differential equations

Gheorghe Craciun, Matthew D. Johnston, Gábor Szederkényi, Elisa Tonello, János Tóth, Polly Y. Yu

Research output: Article


The induced kinetic differential equations of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a system of polynomial differential equations, is it possible to find a network which induces these equations; in other words: is it possible to find a kinetic realization of this system of differential equations? If yes, can we find a network with some chemically relevant properties (implying also important dynamic consequences), such as reversibility, weak reversibility, zero deficiency, detailed balancing, complex balancing, mass conservation, etc.? The constructive answers presented to a series of questions of the above type are useful when fitting differential equations to datasets, or when trying to find out the dynamic behavior of the solutions of differential equations. It turns out that some of these results can be applied when trying to solve seemingly unrelated mathematical problems, like the existence of positive solutions to algebraic equations.

Original languageEnglish
Pages (from-to)862-892
Number of pages31
JournalMathematical Biosciences and Engineering
Issue number1
Publication statusPublished - jan. 1 2020

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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  • Cite this

    Craciun, G., Johnston, M. D., Szederkényi, G., Tonello, E., Tóth, J., & Yu, P. Y. (2020). Realizations of kinetic differential equations. Mathematical Biosciences and Engineering, 17(1), 862-892.