Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationRecent Advances in Delay Differential and Difference Equations
PublisherSpringer New York LLC
Pages105-119
Number of pages15
ISBN (Print)9783319082509
DOIs
Publication statusPublished - Jan 1 2014
EventInternational Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013 - Balatonfured, Hungary
Duration: Jul 15 2013Jul 19 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume94
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013
CountryHungary
CityBalatonfured
Period7/15/137/19/13

    Fingerprint

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hangos, K. M., & Szederkényi, G. (2014). Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations. In 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