Nonlinear systems display a wealth of behaviours and appear a priori unpredictable. Whether they be stochastic or deterministic, nonlinear systems may give rise to unexpected states that can take the form of complex spatiotemporal patterns. The study of such systems is deeply rooted in mathematics and finds high-impact applications in all fields of science and engineering.
The University of Leeds has a long-standing reputation of leading research in the area of nonlinear dynamics. The Centre for Nonlinear Studies (CNLS) was founded in 1984 within the School of Mathematics to enhance existing and foster new collaborations between scientists and engineers. Grown out of CNLS, our group is internationally recognised for our distinctive interdisciplinary approach and for the breadth of our range of expertise. Among other areas, we possess cutting-edge expertise in pattern formation (from quasipatterns to spatial localisation), network dynamics, stochastic processes (e.g. the voter model, agent-based models), physics (from statistical mechanics to fluid dynamics), life sciences and numerical methods, and we are always on the lookout for interesting problems.
We conduct research in many areas. Here are sample questions on which we focus:
- Agent-based models: how to model human behaviour?
- Cultural diversity: how do opinions form and evolve?
- Population dynamics: how do interacting species self-organise?
- Network dynamics: how does network structure affect the diffusion of epidemics?
- Quasipatterns and quasicrystals: how do they form and why are they stable?
- Spatial localisation: how do spatially localised states form in homogeneous systems?
- Nonlinear wave interactions: what role do they play in spatiotemporal chaos?
- Transitional flows: what are the mechanisms that trigger transition to turbulence in fluids?
- Mixing: how can dynamical system theory be turned into fluid mixer design?
- Geometric numerical integration: how to choose a numerical method based on qualitative behaviour?
- Hyperbolic dynamics: what are the most important consequences of non-uniformity?
Should you be interested in any of these investigations, please contact a member of our research group.
We have opportunities for prospective PhD students. Find out more.