### 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 |
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Title of host publication | Recent Advances in Delay Differential and Difference Equations |

Publisher | Springer New York LLC |

Pages | 105-119 |

Number of pages | 15 |

ISBN (Print) | 9783319082509 |

DOIs | |

Publication status | Published - Jan 1 2014 |

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

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 94 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

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

City | Balatonfured |

Period | 7/15/13 → 7/19/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Recent Advances in Delay Differential and Difference Equations*(pp. 105-119). (Springer Proceedings in Mathematics and Statistics; Vol. 94). Springer New York LLC. https://doi.org/10.1007/978-3-319-08251-6_3