Emergent behaviors in adaptive dynamical networks with applications to biological and social systems

Abstract

In this thesis, we consider three network-based systems, focusing on emergent behaviors resulting from adaptive dynamical features.

In our first investigation, we create a model for gene regulatory networks in which the network topology evolves over time to avoid instability of the regulatory dynamics. We consider and compare different rules of competitive edge addition that use topological and dynamical information from the network to determine how new network links are added. We find that aiming to keep connected components small is more effective at preventing widespread network failure than limiting the connections of genes with high sensitivity (i.e., potential for high variability across conditions). Finally, we compare our results to real data from several species and find a trend toward disassortativity over evolutionary time that is similar to our model for structure-based selection.

In our second investigation, we introduce a bidirectional coupling between a phase synchronization model and a cascade model to produce our `sync-contagion' model. The sync-contagion model is well-suited to describe a system in which a contagious signal alerts individuals to realign their orientations, where `orientation' can be in the literal sense (such as a school of fish escaping the threat of a predator) or a more abstract sense (such as a `political orientation' that changes in response to a hot topic). We find that success in realigning the population towards some desired target orientation depends on the relative strengths of contagion spread and synchronization coupling.

In our third and final investigation, we attempt to forecast the complex infection dynamics of the COVID-19 pandemic through a data-driven reservoir computing approach. We focus our attention on forecasting case numbers in the United States at the national and state levels. Despite producing adequate short-term predictions, we find that a simple reservoir computing approach does not perform significantly better than a linear extrapolation. The biggest challenge is the lack of data quantity normally required for machine learning success. We discuss methods to augment our limited data, such as through a `library-based' method or a hybrid modeling approach.