PhD opportunity in Models of Non-Transitive Competition

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 Associate Professor Claire Postlethwaite and Professor Hinke Osinga.

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. The three species, spatially-homogeneous model (“well-mixed” Rock-Paper-Scissors) is well understood, but the addition of spatial dependencies, anisotropies, or additional species results in further complexity. For instance, allowing the populations to diffuse in space can lead to travelling waves, spiral waves and complex dynamics in a partial differential equation model.

The PhD research will focus on the analysis of travelling waves and spiral waves in small competition networks with spatial dynamics. The ideal PhD student will be able to combine cutting-edge mathematical analysis with advanced numerical techniques in order to make predictions about the solutions, such as wavespeeds and wavelengths of travelling waves, or stability of different sizes of spiral waves.

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 seven research-active staff, and numerous PhD students. This project will be in collaboration with Professor Alastair Rucklidge (University of Leeds, UK) and Dr Cris Hasan (University College Cork, Ireland), and there will be opportunities for research visits, 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 August 2022 and March 2023. To apply, candidates should send a cover letter expressing their interest, along with a CV, academic record, and list of three potential referees to Associate Professor Claire Postlethwaite at c.postlethwaite@auckland.ac.nz. Applications will be considered until the position is filled.