Leeds Applied Nonlinear Dynamics

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, the Leeds Applied Nonlinear Dynamics (LAND) group is internationally recognised for its distinctive interdisciplinary approaches and for the breadth of its range of expertise. Among other areas, LAND possesses 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 is always on the lookout for interesting problems.

LAND conducts research in many areas. Here are sample questions on which LAND focuses:

  • 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 do not hesitate to contact the LAND members (links below).

LAND also publishes the quarterly online newsletter UK Nonlinear News and organizes weekly LAND seminars.

Looking for a PhD? Here is a list of positions available within LAND.


Research staff

Dr. Cedric Beaume
Dr. Cédric Beaume
Dr. Richard Mann
Dr. Richard Mann
Dr. Mauro Mobilia
Dr. Mauro Mobilia
Dr. Jitse Niesen
Dr. Jitse Niesen
Prof. Alastair Rucklidge
Prof. Alastair Rucklidge
Dr. Rob Sturman
Dr. Rob Sturman
Dr. Priya Subramanian
Dr. Priya Subramanian
Dr. Jonathan Ward
Dr. Jonathan Ward

PhD students

Ms. Haifaa Alrihieli The Takens–Bogdanov bifurcation in spatially extended pattern formation (Prof. A. Rucklidge)
Mr. Shami Alsallami Modified Hamiltonian in discrete integrable settings (Dr. J. Niesen)
Mr. Giacomo Baldo The evolution of cooperation and coordination (Dr. R. Mann, Dr. S. Azaele, Dr. M. Mobilia)
Ms. Hannah Kreczak Rates of chaotic mixing in models of fluid devices (Dr. R. Sturman and Dr. M. Wilson)
Mr. Andrew Mellor Temporal graph metrics and models (Dr. J. Ward, Prof. A. Rucklidge, Dr. M. Mobilia)
Mr. Anton Pershin Transition to turbulence from spatially localized states (Dr. C. Beaume, Prof. S. Tobias)
Mr. Robert West Dynamics of the cyclic Lotka–Volterra and Rock-Paper-Scissors models (Dr. M. Mobilia, Prof. A. Rucklidge)
Mr. Patrick Wright Return times for toral linked twist maps (Dr. R. Sturman, Dr. J. Niesen)