Analysis of Qualitative Dynamic Properties of Positive Polynomial Systems Using Transformations
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.
KeywordsPolynomial ODEs Positive systems Dynamic equivalence Dynamic similarity Structural stability
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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