### Abstract

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 language | English |
---|---|

Pages (from-to) | 862-892 |

Number of pages | 31 |

Journal | Mathematical biosciences and engineering : MBE |

Volume | 17 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 6 2019 |

### Fingerprint

### Keywords

- kinetic equations
- mass action kinetics
- reaction networks
- realizations
- reversibility
- weak reversibility

### ASJC Scopus subject areas

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

### Cite this

*Mathematical biosciences and engineering : MBE*,

*17*(1), 862-892. https://doi.org/10.3934/mbe.2020046

**Realizations of kinetic differential equations.** / Craciun, Gheorghe; Johnston, Matthew D.; Szederkényi, Gábor; Tonello, Elisa; Tóth, János; Yu, Polly Y.

Research output: Contribution to journal › Article

*Mathematical biosciences and engineering : MBE*, vol. 17, no. 1, pp. 862-892. https://doi.org/10.3934/mbe.2020046

}

TY - JOUR

T1 - Realizations of kinetic differential equations

AU - Craciun, Gheorghe

AU - Johnston, Matthew D.

AU - Szederkényi, Gábor

AU - Tonello, Elisa

AU - Tóth, János

AU - Yu, Polly Y.

PY - 2019/11/6

Y1 - 2019/11/6

N2 - 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.

AB - 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.

KW - kinetic equations

KW - mass action kinetics

KW - reaction networks

KW - realizations

KW - reversibility

KW - weak reversibility

UR - http://www.scopus.com/inward/record.url?scp=85075055994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075055994&partnerID=8YFLogxK

U2 - 10.3934/mbe.2020046

DO - 10.3934/mbe.2020046

M3 - Article

C2 - 31731382

AN - SCOPUS:85075055994

VL - 17

SP - 862

EP - 892

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 1

ER -