Stochastic simulation, analysis, and inference of non-linear dynamical systems

This project aims to create a new framework for studying the dynamics of systems that exhibit periodic behaviour or multiple equilibria. These types of dynamic behaviours are common in various fields such as molecular biology and epidemiology. Examples include the circadian clocks, oscillatory responses to stress signals, and the specialisation of stem cells, as well as epidemic oscillations driven by public awareness. To build this framework, the project will utilize the theory of dynamical systems, which allows for the decomposition of large, non-linear dynamical systems into simpler components of smaller dimensions. The project will also develop stochastic models that accurately describe stochastic dynamics, while being computationally fast for simulation, sensitivity analysis and Bayesian inference of model parameters using time-series data. The ideal candidate for this project will have strong interest in stochastic dynamical systems, molecular biology and/or epidemiology, and will possess strong programming abilities. While a background in stochastic processes (e.g. Markov processes, stochastic differential equations) or non-linear dynamical systems will be beneficial, candidates with a strong background in other mathematical subjects will also be considered.

Funding Notes

Fully funded scholarship places (fees, plus stipend of approx. £19,775) are typically available for well-qualified students. UK, EU and other overseas students are all encouraged to apply. Further details of the application and selection procedure are at View Website (pdf - see last page) and View Website.

References

Frederick Truman-Williams and Giorgos Minas (2025), Simulating stochastic population dynamics: The Linear Noise Approximation can capture non-linear phenomena, https://arxiv.org/abs/2504.15166
Swallow, B., Rand, D. A., & Minas, G. (2024). Bayesian Inference for Stochastic Oscillatory Systems Using the Phase-Corrected Linear Noise Approximation. Bayesian Analysis., 1(1). https://doi.org/10.1214/24-BA1471