This thesis is divided into five chapters and is the result of the research I carried out during my time as a PhD student at Imperial College London.
In chapter 1, I introduce the results of my research and place my work in the context of the existing literature.
In chapter 2, I present a novel method to analyse the critical behaviour of complex systems and discuss its application to three case studies: two from equilibrium statistical mechanics (the Ising Model and the XY Model) and one from self-organised criticality (the Forest Fire Model).
In chapter 3, I focus my attention on the Forest Fire Model and discuss its relevance for the study of real systems, like the brain and rain precipitation. I also analyse the distribution of the largest cluster and show that it displays a behaviour that is consistent with the observations done in chapter 2.
In chapter 4, I introduce an agent-based model of financial networks which is inspired by the Tangled Nature Model of evolutionary ecology. This model can qualitatively reproduce the evolution of the number of banks in the U.S. and the behaviour of the firm size distribution observed in different countries. I also discuss the effectiveness of Quantitative Easing in dealing with financial crashes and present information-theoretic measures that could be used to track, and possibly prevent, the development of the instabilities leading to a crash.
In chapter 5, I summarise my results and discuss some possible research that could be fostered by this thesis.