"Chemical reactions network theory (CRNT) analysis and applications of " by Daryl M. Magpantay

Chemical reactions network theory (CRNT) analysis and applications of poly-pl kinetic system

Date of Publication

8-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Ederlina G. Nocon
Eduardo R. Mendoza

Defense Panel Member

Angelyn Lao
Noel T. Fortun
Yvette F. Lim
Luis F. Razon
Editha C. Jose

Abstract/Summary

Evolutionary Game Theory (EGT) models the evolutionary phenomenon through a replica- tor system that is based on the polynomial payoff functions. It is a polynomial dynamical

system of ordinary differential equations that analyzes strategies that prove to be beneficial under certain conditions. In the study of Veloz et al., they proposed to analyze the dynamics of EGT models using Chemical Reaction Network Theory (CRNT) in the form of polynomial kinetics (POK). In CRNT, topological properties of the dynamical systems are studied and analyzed. From the CRNT point of view, it now becomes interesting to study a superset of POK, which we call poly-PL kinetics (PYK). This set is formed by getting nonnegative linear combinations of power law functions. Since only CRNs with mass-action (MAK) and power-law kinetics (PLK) are currently available, PYKs are transformed into PLK. In this

study, we present two approaches on how these transformations can be done. In the first ap- proach, we use a network structure-oriented transformations using the S-invariant term-wise

addition of reactions, which we denoted as STAR. Whereas in the second approach, it is via Craciun’s Euclidean embedded graph (E- graph). Here, polynomial dynamical system can be regarded as being generated by some E-graph. Results on positive equilibria of PYK systems based on the associated E-graph are discussed. Aside from the transformation approaches, another pioneering work on PYK (to our knowledge) of this study is the qualitative analysis of certain poly-PL kinetics systems and its application to polynomial replicator systems. We are able to identify a class of poly-PL which have zero kinetic reactant deficiency, an important criteria for the existence of complex balanced equilibria.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG008250

Keywords

Chemical reactions; Chemical kinetics

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Embargo Period

3-30-2025

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