### Abstract

Two classes of positive polynomial systems, quasi-polynomial (QP) systems and reaction kinetic networks with mass action law (MAL-CRN), are considered. QP systems are general descriptors of ODEs with smooth right-hand sides; their stability properties can be checked by algebraic methods (linear matrix inequalities). On the other hand, MAL-CRN systems possess a combinatorial characterization of their structural stability properties using their reaction graph. Dynamic equivalence and similarity transformations applied either to the variables (quasi-monomial and time-reparametrization transformations) or to the phase state space (translated X-factorable transformation) will be applied to construct a dynamically similar linear MAL-CRN model to certain given QP system models. This way one can establish sufficient structural stability conditions based on the underlying reaction graph properties for the subset of QP system models that enable such a construction.

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

Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 105-119 |

Number of pages | 15 |

Volume | 94 |

ISBN (Print) | 9783319082509 |

DOIs | |

Publication status | Published - 2014 |

Event | International Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013 - Balatonfured, Hungary Duration: Jul 15 2013 → Jul 19 2013 |

### Other

Other | International Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013 |
---|---|

Country | Hungary |

City | Balatonfured |

Period | 7/15/13 → 7/19/13 |

### Fingerprint

### Keywords

- Dynamic equivalence
- dynamic equivalence Dynamic similarity
- Polynomial ODEs
- Positive systems
- Structural stability

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Springer Proceedings in Mathematics and Statistics*(Vol. 94, pp. 105-119). Springer New York LLC. https://doi.org/10.1007/978-3-319-08251-6_3

**Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations.** / Hangos, K.; Szederkényi, G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Springer Proceedings in Mathematics and Statistics.*vol. 94, Springer New York LLC, pp. 105-119, International Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013, Balatonfured, Hungary, 7/15/13. https://doi.org/10.1007/978-3-319-08251-6_3

}

TY - GEN

T1 - Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations

AU - Hangos, K.

AU - Szederkényi, G.

PY - 2014

Y1 - 2014

N2 - Two classes of positive polynomial systems, quasi-polynomial (QP) systems and reaction kinetic networks with mass action law (MAL-CRN), are considered. QP systems are general descriptors of ODEs with smooth right-hand sides; their stability properties can be checked by algebraic methods (linear matrix inequalities). On the other hand, MAL-CRN systems possess a combinatorial characterization of their structural stability properties using their reaction graph. Dynamic equivalence and similarity transformations applied either to the variables (quasi-monomial and time-reparametrization transformations) or to the phase state space (translated X-factorable transformation) will be applied to construct a dynamically similar linear MAL-CRN model to certain given QP system models. This way one can establish sufficient structural stability conditions based on the underlying reaction graph properties for the subset of QP system models that enable such a construction.

AB - Two classes of positive polynomial systems, quasi-polynomial (QP) systems and reaction kinetic networks with mass action law (MAL-CRN), are considered. QP systems are general descriptors of ODEs with smooth right-hand sides; their stability properties can be checked by algebraic methods (linear matrix inequalities). On the other hand, MAL-CRN systems possess a combinatorial characterization of their structural stability properties using their reaction graph. Dynamic equivalence and similarity transformations applied either to the variables (quasi-monomial and time-reparametrization transformations) or to the phase state space (translated X-factorable transformation) will be applied to construct a dynamically similar linear MAL-CRN model to certain given QP system models. This way one can establish sufficient structural stability conditions based on the underlying reaction graph properties for the subset of QP system models that enable such a construction.

KW - Dynamic equivalence

KW - dynamic equivalence Dynamic similarity

KW - Polynomial ODEs

KW - Positive systems

KW - Structural stability

UR - http://www.scopus.com/inward/record.url?scp=84906849113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906849113&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-08251-6_3

DO - 10.1007/978-3-319-08251-6_3

M3 - Conference contribution

SN - 9783319082509

VL - 94

SP - 105

EP - 119

BT - Springer Proceedings in Mathematics and Statistics

PB - Springer New York LLC

ER -