Models of complex adaptive systems with underlying network structure

Thesis

This thesis explores the effect of different types of underlying network structure on the dynamical behaviour of a competitive population - a situation encountered in many real-world complex systems. In the first part of the thesis, I focus on generic, but abstract, multi-agent systems. I start by presenting analytic and numerical results for a population of heterogeneous, decision-making agents competing for some limited global resource, in which connections arise unintentionally between agents as a by-product of their strategy choices. I show that accounting for the resulting groups of strongly-correlated agents - in particular, the crowds and so-called 'anticrowds' - yields an accurate analytic description of the systems dynamics. I then introduce a local communication network between the agents, enabling them to intentionally share information among themselves. Such an interaction network leads to highly non-trivial dynamics, forcing a trade-off between individual and global success. Introducing corruption into the information being exchanged between agents, gives rise to a novel phase transition. I then provide a quantitative analytic theory of these various numerical results by generalizing the Crowd-Anticrowd formalism to include such local interactions.

In the second part of the thesis, I consider a real-world system which also features competitive populations and networks - a cancer tumour, which contains cancerous cells competing for space and nutrients in the presence of an underlying vasculature structure. To simplify the analysis and comparison to real clinical data, the model chosen is far simpler than that discussed in the first part of the thesis - however despite its simplicity, the model is shown to yield remarkably good agreement with empirical findings. In addition, the model shows how different treatment methods can lead to a wide variety of unexpected re-growth behaviours of the tumour.

Authors: Choe, S

• DOI: 10.5287/ora-6rkmrxqvy
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford