Applications are invited for a fully-funded PhD scholarship in Applied Dynamical Systems in the Department of Mathematics at the University of Auckland, New Zealand. The project will be supervised by Professor Claire Postlethwaite.
Project outline
Interactions between plant and animal species have long been known to cause oscillations, or cyclical behaviour, in species population densities. We are interested in particular in so-called intransitive competition between species. Here, each species has both advantageous and disadvantageous traits, and no single species dominates. This type of competition, exemplified by the game of Rock-Paper-Scissors, is thought to increase biodiversity, as no single species is the “best” competitor.
Mathematical models of such competition can contain objects called heteroclinic networks, close to which the dynamics of the system are intermittent. Typically, one species dominates for a while, then another, and so on, resulting in a sequence of dominating species. This behaviour of such systems is well-understood in the simplest scenario of three species interacting as in the game of Rock-Paper-Scissors. In more realistic scenarios with additional species, the sequence of dominating species can be remarkably complex, possibly chaotic, in which case the switching between which species dominates, and the lengths of time each dominates for, becomes unpredictable.
The PhD research will focus on analysing the dynamics of heteroclinic networks using techniques from the theory of piecewise-smooth dynamical systems, which allow us to reduce the dimension of the dynamics whilst retaining the information about how the trajectories switch around the network. The ideal PhD student will be able to combine cutting-edge mathematical analysis with advanced numerical techniques. The results of the research will have application to both ecological and economic game theory.
Other information
Successful candidates will hold, or expect to complete soon, a Bachelor’s or Master’s degree in Pure or Applied Mathematics, or similar. They should have a strong background in dynamical systems and computational mathematics.
You will work within the dynamical systems group at the University of Auckland. The group currently has eight research-active staff, and numerous PhD students. This project will be in collaboration with Associate Professor David Simpson (Massey University, Palmerston North), and there will be opportunities for research visits to other collaborators in the UK, such as Professor Alastair Rucklidge (University of Leeds) and Professor Paul Glendinning (University of Manchester), as well as participation in international conferences to present your PhD research.
Applicants from all countries and backgrounds are actively encouraged to apply. Members of underrepresented groups are very welcome, as are students with families. Our research group aims to achieve work-life balance within a productive scientific environment. Informal enquiries are welcome by email, to Claire Postlethwaite (c.postlethwaite@auckland.ac.nz)
Stipend is NZ$35,000 pa (tax free) for three years plus tuition fees (domestic or international). Start date is flexible but would preferably be between March and October 2026. To apply, candidates should send a cover letter expressing their interest and explaining why they think they would be suited for the project, along with a CV, academic record, and list of three potential referees to Professor Claire Postlethwaite at c.postlethwaite@auckland.ac.nz. Applications will be considered until the position is filled.