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arXiv · 1907.07266

Realizations of kinetic differential equations

G. Craciun·M. D. Johnston·G. Szederkényi·E. Tonello·J. Tóth·P. Y. Yu
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Abstract

The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible to find a network which induces the equation? 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 a differential equation to measurements, or when trying to find out the dynamic behavior of the solutions of a differential equation. It turns out that some of the results can be applied when trying to solve purely mathematical problems, like the existence of positive solutions to polynomial equation.

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G. Craciun, M. D. Johnston, G. Szederkényi, E. Tonello, J. Tóth, P. Y. Yu. 2019-07-16. Realizations of kinetic differential equations. https://arxiv.org/abs/1907.07266

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