Beyond Pairwise Interactions: Exploring Higher-Order Dynamics in Complex Systems

About the Project

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.

Complex systems are everywhere — from swarming birds and interacting cells to the spread of ideas or diseases through society. In each case, countless individuals interact to produce collective behaviours far more intricate than the actions of any single part. As Stephen Hawking remarked in 2000, “I think the next century will be the century of complexity.”

This PhD project explores one of the most exciting frontiers in this field: higher-order interactions. Traditional models describe systems through pairwise links between individuals, like edges in a network. Yet many real-world phenomena — such as collective decision-making, cooperation, or social contagion — depend on group interactions involving three or more participants. Capturing these dynamics requires new mathematical frameworks that move beyond simple networks.

You will develop and simulate models of interacting agents that include higher-order mechanisms and study how these give rise to novel, emergent behaviours. The resulting synthetic datasets will be analysed using tools from information theory, network science, and complex systems modelling. You will also explore new ways to represent group interactions using hypergraphs and simplicial complexes.

Finally, the developed methods will be applied to real-world biological data, such as the collective motion of insects studied within our research group.

This interdisciplinary project is ideal for students in applied mathematics, physics, or related quantitative disciplines who are curious about how simple rules can generate rich collective phenomena — and who want to help shape the next generation of complexity science.

Informal enquiries can be made by contacting Dr Perez-Reche (fperez-reche@abdn.ac.uk)

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in mathematics, physics or related quantitative disciplines.

We encourage applications from all backgrounds and communities, and are committed to having a diverse, inclusive team.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Degree of Doctor of Philosophy in Physics to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project titleon the application form. If you do not include these details, it may not be considered for the project.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts .

Please note: you do not need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at researchadmissions@abdn.ac.uk

Funding Notes

This is a self-funding project open to students worldwide. Our typical start dates for this programme are February or October.

Fees for this programme can be found here Finance and Funding | Study Here | The University of Aberdeen.