Decomposition classes and the structure and dynamics of reaction networks - Fontanil, Lauro L. (Animo Repository, 2021)
Many recent studies on Chemical Reaction Network Theory indicate that there is a renewed interest in network decomposition. These studies demonstrate the usefulness of decomposition in answering various problems about chemical reaction networks (CRNs). This thesis aims to contribute to this growing initiative by providing a study of important properties commonly shared by a CRN and its subnetworks. First, this study catalogues graph-theoretic properties (when a reaction network is viewed as a directed graph) and stoichiometric properties (when the reactions are considered as vectors in a Euclidean space) that can be lifted from the subnetworks to the parent network and vice versa. Second, the set of common complexes of subnetworks are associated with relevant properties including the so-called incidence-independence property, which has important implications on the capacity of a CRN to admit complex balanced equilibria. Finally, this study offers algorithms, based on existing theorems, that identify concentration robustness in CRNs by taking advantage of network decomposition. Overall, this thesis reiterates the relevance of decomposition of CRNs to study rich phenomena in networks by exposing interesting features of decomposition that were not considered in other studies.