Research Interests

Nonlinear Partial Differential Equations, Pattern formation, Bifurcation theory, Numerical Analysis.

Further details can be found on my personal web page.

Publications

G Faye, J Rankin and DJB Lloyd, Localized radial bumps of a neural field equation on the Euclidean plane and the Poincare disk, Nonlinearity 26 (2013) 437-478, pdf

2.DJB Lloyd and H O’Farrell, On localised hotspots of an urban crime model, Submitted, 2012, pdf

A.C. Skeldon, G. Chaffey, D.J.B. Lloyd, V. Mohan, D. Bradley and A. Nisbet, Modelling and detecting tumour oxygenation levels, PLoS ONE 7(6): e38597, 2012, pdf

J Chamard, J Otta and DJB Lloyd, Computation of Minimum Energy Paths for Quasi-Linear Problems, Springer J. Scientific Computing 49(2), 180-194, 2011, pdf

H Shiozawa, AC Skeldon, DJB Lloyd, V Stolojan, DC Cox, SRP Silva, Spontaneous Emergence of Long-range Shape Symmetry, Nanoletters 11(1) 160-163 (2011). Preprint, Supplementary material

J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht, Isolas of 2-pulse solutions in homoclinic snaking scenarios, JDDE 23 93-114 (2011), pdf

D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede, To snake or not to snake in the planar Swift-Hohenberg equation, SIAM Journal on Applied Dynamical Systems 9 (2010) 704-733, pdf, movie_nonlocalised_stripes.mpg, movie_change_curvature.mpg

E Dalah, D Bradley, D Lloyd, AC Skeldon and A Nisbet, Simulating the heterogeneous distribution of O_2 partial pressure in 2D vasculature using a reaction-diffusion model, Submitted, 2009 pdf

DJB Lloyd, B Sandstede, Localized radial solutions of the Swift–Hohenberg equation, Nonlinearity 22(2) 485–524, 2009, pdf

M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht, Snakes, ladders, and isolas of localised patterns, SIAM J. Math. Anal. 41(3) 936-972, 2008, pdf

DJB Lloyd, B Sandstede, D Avitabile and AR Champneys, Localized hexagon patterns in the planar Swift-Hohenberg equation, SIAM J. Appl. Dyn. Sys. 7(3) 1049-1100, 2008. pdf, hexagon movie, ladder movie

DJB Lloyd, AR Champneys and RE Wilson, Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation, Physica D, 204 (3-4):240-268, 2005.

DJB Lloyd and AR Champneys, Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons, SIAM Journal of Scientific Computing, 27 (3):759-773, 2005.

Teaching

In Spring 2009, I teach MAT1029 Experiment.

PhD Projects

I am happy to discuss possible PhD projects. Available projects can be found here.