Author ORCID Identifier
Semester
Fall
Date of Graduation
2025
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Casian Pantea
Committee Co-Chair
Adam Halasz
Committee Member
Adrian Tudorascu
Committee Member
Charis Tsikkou
Committee Member
Vyacheslav Akkerman
Abstract
Weakly reversible, deficiency zero (WR0) systems form a large class of polynomial ODEs modeling chemical reaction networks. Their behavior is exceptionally stable: they have unique positive steady states, which are locally asymptotically stable (they are also conjectured to be globally asymptotically stable). This powerful result (the Deficiency Zero Theorem) applies to a large class of high dimensional, nonlinear polynomial dynamics, and is independent of the choice of parameters in the model. In this dissertation we present two algorithms that expands the scope of the Deficiency Zero Theorem to:
1. Networks with WR0 realizations, i.e. networks that are not necessarily WR0 but have the same ODEs as a WR0 system for any choice of parameters.
2. ODE systems with WR0 realizations, i.e. ODE systems that model WR0 networks under certain conditions on the parameters.
In the first algorithm, we output the underlying network of the WR0 realization. In the second algorithm, we output the underlying network of each WR0 realization.
Additionally, in the second algorithm, for each network, we output the conditions on the parameters under which it is a realization of the ODE system. Alongside these algorithms, we will discuss the key concepts in reaction network theory and polyhedral geometry associated with these algorithms.
Recommended Citation
Buxton, Neal Ryan, "Weakly Reversible Deficiency Zero Realizations of Polynomial Dynamical Systems" (2025). Graduate Theses, Dissertations, and Problem Reports. 13133.
https://researchrepository.wvu.edu/etd/13133