Abstract
As human beings, we now live in a hybrid—physical and virtual—environment. These environments are characterised by many interactions among different units or agents across varied times and scales. This is typical of complex systems, which often demonstrate an emergent collective behaviour that differs from any individual agent's behaviour. However, these interactions often yield complicated phenomena that cannot easily be interpreted using conventional mathematical or physical methodologies. Sometimes, it is even challenging to figure out what to look at in complex systems. Notably, as a rapidly growing area, complex systems science has attracted so much attention from academia and industry that researchers from multidisciplinary backgrounds are trying to decipher the unknowns in various complex systems, such as ecological and financial systems. To quantify the details of a complex system, it is essential first to know the topology, i.e., who interacts with who, and then the dynamics, i.e., how the individual agents behave and interact. Based on these understandings, agent-based modelling and data analysis can play key roles in investigating complex systems.In this thesis, we consider two different perspectives to studying complex systems—data-driven and model-led. The data-driven way is to discover the hidden patterns in a system by analysing the outcomes, i.e., the data generated by the system. The model-led way claims that we can investigate the dynamics of a system by building theoretical models and then observing and analysing their dynamics. Additionally, we use information from the networks of the associated systems to conduct spectral analysis, which is an analogy to data analysis of the system, to extrapolate the patterns in them.
We first show, in Chapters 3 and 4, how complex systems can be studied from the data-driven way. In two different complex systems, the collective motion of fish schools and pedestrians, we demonstrate that if we only know the outcomes, i.e. the trajectory data of individuals, we can still structure the interactions as a network, and apply network-based data analysis methods to uncover the driven variables and hidden patterns in the system. Complex systems can also be investigated from the model-led way, as Chapter 5 and 6 indicate. In these two chapters, we use agent-based modelling and game theoretic techniques to explore cooperative behaviours and spatial patterns, such as wave instabilities on networks in the context of ecological systems, in which each patch can harbour various agents while connecting to other patches to construct a spatial network.
In all four works described in Chapters 3-6, we also demonstrate that the topological information encoded in the data produced by agents in complex systems can be used to structure the interactive relations of agents, or sometimes the habitats of agents in the systems, as a network. These networks either relate to direct interactions of agents in the system or indirect interactions of agents that can be linked due to similar behaviour styles.
This thesis covers the theories and applications of complex systems, enabling us to conduct a multi-scale analysis of various systems. The mathematical tools and the general frameworks we propose to study complex systems can be transferred to broader areas that need to tackle complexities. Overall, exploring how such analyses, such as identifying driven variables, and investigating pattern formations and dynamics in complex systems, can generate many insights and benefits for us to understand our world.
| Date of Award | 24 Jan 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Martin E Homer (Supervisor) & Nikolai W F Bode (Supervisor) |