# Realizations of kinetic differential equations

Source: [Realizations of kinetic differential equations](<https://www.sota2.com/research/paper/68fa562b1e209131ce99a6f0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:59:48.577Z

Authors: G. Craciun, M.D. Johnston, G. Szederk\\'enyi, E. Tonello, J. T\\'oth, P.Y. Yu

Published: 2019-07-16T21:23:11.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1907.07266>)

[PDF](<https://arxiv.org/pdf/1907.07266.pdf>)