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Polynomial Dynamical Systems & Interaction Network Models
Başlık:
Polynomial Dynamical Systems & Interaction Network Models
Yazar:
Brunner, James D., author.
ISBN:
9780355941111
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (125 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Gheorghe Craciun Committee members: David F. Anderson; Daniele Cappelletti; Daniel M. Erman.
Özet:
A persistent dynamical system in positive phase space is one whose solutions have positive lower bounds for large t, while a permanent dynamical system in positive phase space is one whose solutions have uniform upper and lower bounds for large t. These properties have important applications for the study of mathematical models in biochemistry, cell biology, and ecology. Inspired by reaction network theory, we define a class of polynomial dynamical systems called tropically endotactic. We show that two-dimensional tropically endotactic polynomial dynamical systems are permanent, irrespective of the values of (possibly time-dependent) parameters in these systems. These results generalize the permanence of two-dimensional reversible, weakly reversible, and endotactic mass action systems.
We define two important tools in the analysis of polynomial dynamical systems, the Euclidean embedded graph (E-graph) and the Dominance Differential Inclusion. We present a construction for the Dominance Differential Inclusion, and we prove that any system generated by the E-graph can be embedded into this differential inclusion, and that it is in some sense the "minimal" differential inclusion with that property.
Furthermore, we present an overview of the classical results of chemical reaction network theory, and present some examples of interest.
Notlar:
School code: 0262
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(681532.1) | 681532-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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