EPSRC DTP PhD studentship: Mathematical modelling of cognitive behaviour using network attractors

University of Exeter - College of Engineering, Mathematics and Physical Sciences

Main supervisor:  Peter Ashwin (University of Exeter)

This project will examine a novel approach to modelling changes in perception via classes of nonlinear differential equations/dynamical systems, where the attracting behaviour consists of heteroclinic networks (also called “winnerless competition” behaviour of neural groups). This type of dynamics is complex and well-studied but not chaotic in the usual sense of, e.g., density of periodic orbits or expansion of nearby orbits. Perceptual rivalry is a phenomenon in cognitive neuroscience where the perception of the brain spontaneously and repeatedly changes between plausible interpretations of conflicting inputs, and the effect is exploited in several optical illusions such as the “Necker cube”. The project will aim to understand this in terms of nonlinear dynamical systems in the presence of noise and inputs that may be conflicting; this includes cases where there may be three or more possible states of perception. The project may interact with potential collaborators in Barcelona (Huguet and Guillamon) who are experts in mathematical modelling of perceptual rivalry and with a current collaborator in Auckland (Postlethwaite) – this project very much builds on recent joint work with Postlethwaite.

There will be an initial period of training in nonlinear dynamics and the modelling of neural systems. The student will commence original study on a number of possible dynamical models to explain multi-state perceptual rivalry. These include fairly standard “potential landscape” dynamics that are used in the literature (but far from properly explored) to more novel “network attractors” that have been developed by the supervisor and Postlethwaite in the last few years

The student will be able to interact with a variety of other students and academics in Exeter – in particular in the Dynamical Systems and the Biomedical Modelling research groups, and especially the Centre for Predictive Modelling in Healthcare. They will benefit from training in a range of methods (from rigorous estimation of scaling laws in stochastically perturbed systems to numerical modelling of nonlinear systems). The particular emphasis would be tailored to the student’s interests.

3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,296 per year.

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South West England