Positive Network Systems : Heuristic Methods and Opinion Dynamics

The analysis of interconnected systems is a large and growing field, with successful applications in a wide range of natural and synthesized systems. Biomolecular networks, power grids and human social dynamics have all been the subject of study through the lens of network dynamics, with impressive results. The work presented in this thesis takes the form of four research papers all focusing in different ways on networks. These networks consist of simple systems, which interact to give rise to more complex dynamics. The first and second papers deal with methods for controlling interconnected positive linear systems in ways that remain viable as the scale of the system grows. In the third and fourth papers, models for opinion dynamics are constructed by extending existing linear and positive models, using nonlinearities to capture more complex behavior. Specifically, this enables asymptotic disagreement, or dissensus, between agents as the dynamics evolve.