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PhD Studentship: Modelling Convergent, Divergent and Oscillatory Phenomena in Social Dynamics

University of Birmingham - School of Mathematics

Qualification Type: PhD
Location: Birmingham
Funding for: UK Students
Funding amount: This is a fully funded PhD project available to any Home (UK) student with a strong background in applied mathematics or a related discipline.
Hours: Full Time
Placed On: 7th December 2023
Closes: 7th March 2024

If you are interested in building mathematical models to explain social phenomena in a variety of contexts, from flocking animals to interacting crowds, and you have a strong academic background in applied mathematics or a related discipline, then this project could be perfect for you.

For our purposes, an agent-based model (ABM) of social dynamics refers to a high-dimensional nonlinear dynamical system, in continuous or discrete time, where every variable is assigned a deterministic or stochastic evolution law derived from sociological assumptions. A typical ABM assigns laws that are simple and universal, describing the pairwise interactions among agents and leading to emergent collective behaviours of the whole population. For bird flocks, the variables are positions and velocities of individual birds while the evolution laws may dictate that every bird tries to align its velocity with those of its neighbours (Cucker & Smale, 2007). This model posits an explanation for the collective behaviour of “flocking”, where all birds’ velocities converge to a common value.

In five decades of development, the field has produced myriad ABMs to explain convergent behaviour while theories of non-convergent phenomena remain under-developed. In this project, you will develop ABMs to unify the explanatory framework for convergent and non-convergent phenomena. Where appropriate, the recent model by Stokes et al. (2022), which explained oscillatory opinion clusters, will be extended. The resulting framework may offer unique insights into many open questions in social dynamics and the field of complex systems more generally. For example, in bird flocks, what mechanisms give rise to transient patterns such as those commonly seen in a starling murmuration (Ballerini et al., 2008)? In human societies, what drives opinion polarisation and what kinds of population-level behaviour can emerge from interacting with polarised factions (Sobkowicz, 2020)?

Informal enquiries are encouraged – please get in touch for further information with the project supervisors with Dr Galane Luo (g.j.luo@bham.ac.uk).

Funding notes:

This is a fully funded PhD project available to any Home (UK) student with a strong background in applied mathematics or a related discipline.

References:

Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A. and Viale, M., 2008. Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the national academy of sciences, 105(4), pp.1232-1237.

Cucker, F. and Smale, S., 2007. Emergent behavior in flocks. IEEE Transactions on automatic control, 52(5), pp.852-862.

Sobkowicz, P., 2020. Whither Now, Opinion Modelers?. Frontiers in Physics, 8, p.587009.

Stokes, B.M., Jackson, S.E., Garnett, P. and Luo, J., 2022. Extremism, segregation and oscillatory states emerge through collective opinion dynamics in a novel agent-based model. The Journal of Mathematical Sociology, pp.1-39.

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