Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations

Research output: Conference 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 publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages105-119
Number of pages15
Volume94
ISBN (Print)9783319082509
DOIs
Publication statusPublished - 2014
EventInternational Conference on Delay Differential and Difference Equations and Applications, ICDDDEA 2013 - Balatonfured, Hungary
Duration: júl. 15 2013júl. 19 2013

Other

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

Fingerprint

Positive Polynomials
Positive Systems
Polynomial Systems
Qualitative Properties
Dynamic Properties
Structural Stability
Equivalence Transformations
Reparametrization
Reaction Kinetics
Similarity Transformation
Algebraic Methods
Monomial
Graph in graph theory
Stability Condition
Descriptors
Matrix Inequality
Linear Inequalities
Phase Space
State Space
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

Springer Proceedings in Mathematics and Statistics. Vol. 94 Springer New York LLC, 2014. p. 105-119.

Research output: Conference contribution

Hangos, K & Szederkényi, G 2014, Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations. in 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
Hangos K, Szederkényi G. Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations. In Springer Proceedings in Mathematics and Statistics. Vol. 94. Springer New York LLC. 2014. p. 105-119 https://doi.org/10.1007/978-3-319-08251-6_3
Hangos, K. ; Szederkényi, G. / Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations. Springer Proceedings in Mathematics and Statistics. Vol. 94 Springer New York LLC, 2014. pp. 105-119
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