Matt Johnston, PhD Candidate
Department of Applied Mathematics, University of Waterloo
Under suitable assumptions the dynamics of chemical reaction networks is governed by a set of autonomous, polynomial ordinary differential equations where the quantities of concern are the specie concentrations. In general these systems are highly nonlinear and difficult to analyze; however, easily verifiable conditions are known under which many strong dynamical properties hold.
In this talk, I will focus on the relationship between the topological structure of a chemical reaction network and the dynamics of the network. In particular, I will introduce conditions on the reaction graph under which a reaction graph with "bad" structure can be transformed into one with "good" structure while preserving qualitative aspects of the dynamics. I will also give an algorithm capable of finding conjugate networks within a specific class of networks with known dynamics.