Dynamical Grouping in Complex Systems

of a dissertation at the University of Miami. Dissertation supervised by Professor Neil F. Johnson. No. of pages in text. (183) Quantifying the behavior of complex systems arguably presents the common “hard” problem across the physical, biological, social, economic sciences [1]. Individual-based or agent-based models have proved useful in a variety of different real world systems: from the physical, biological, medical domains through to social and even financial domains. There are many different models in each of these fields, each with their own particular assumptions, strengths and weaknesses for particular application areas. However, there is a lack of minimal model analysis in which both numerical and analytic results can be obtained, and hence allowing different application domains to be analyzed on a common footing. This thesis focuses on a few simple, yet highly non-trivial, minimal models of a population of interacting objects (so-called agents) featuring internal dynamical grouping. In addition to analyzing these models, I apply them to a number of distinct real world systems. Both the numerical and analytical results suggest that these simple models could be key factors in explaining the overall collective behavior and emergent properties in a wide range of real world complex systems. In particular, I study variants of a particular model (called the EZ model) in order to explain the attrition time in modern conflicts, and the evolution of contagion phenomena in such a dynamically evolving population. I also study and explain the empirical data obtained for online guilds and offline gangs, leading to a team-based model which captures the common quantitative features of the data. I then move on to develop a resource competition model (i.e. the so-called El Farol model) and apply it to the carbon emissions market, mapping the different market factors into model parameters which enable me to explore the potential market behaviors under a variety of