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Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations

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Recent Advances in Delay Differential and Difference Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 94))

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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.

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Acknowledgements

This paper is dedicated to Prof. István Győri on the occasion of his 70th birthday. This research has been supported by the Hungarian National Research Fund through grants NF104706 and K83440.

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Authors and Affiliations

  1. University of Pannonia, Veszprém, Hungary

    Katalin M. Hangos

  2. Computer and Automation Research Institute, Budapest, Hungary

    Katalin M. Hangos

  3. Faculty of Information Technology, Peter Pázmány Catholic University, Budapest, Hungary

    Gábor Szederkényi

Authors
  1. Katalin M. Hangos
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  2. Gábor Szederkényi
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Correspondence to Katalin M. Hangos .

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Editors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Ferenc Hartung

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Mihály Pituk

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Hangos, K.M., Szederkényi, G. (2014). Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations. In: Hartung, F., Pituk, M. (eds) Recent Advances in Delay Differential and Difference Equations. Springer Proceedings in Mathematics & Statistics, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-08251-6_3

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