+44 1865 615166
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
I am broadly interested in nonlinear dynamical systems, with applications to mathematical biology and other areas. I am particularly interested in understanding and overcoming the limits of current methodologies to capture spatial and temporal complexity in situations of scientific interest. I am currently active in the following research areas:
- Reaction-Diffusion Systems: pattern formation, diffusion-driven (Turing) instabilities, spatiotemporal phenomena (including chaos and heterogeneity), RD systems on static and growing manifolds, with applications to developmental biology, population dynamics, and tissue engineering.
- Spatial Population Dynamics: discrete patch and spatially continuous models, random and deterministic dispersal, synchronization of metapopulations, and applications to ecological and epidemiological metapopulation models.
Nonlinear Dynamical Systems: dissipative dynamics (attractors and absorbing sets), numerical bifurcation analysis, and stochastic differential equations.
In all of these cases I am interested both in the scientific field or application, as well as in the theoretical or computational tools used. I primarily approach problems from a dynamical systems point of view, and I am keen to see applications motivate new theory in this field. However, I am much more motivated by developing approaches to solve problems as they are, rather than trying to force them into a particular shape in order to use a specific hammer. While I have used several tools in the past, I am more than happy to pick up new methodologies in order to address an interesting problem. I am also happy to pursue questions outside of my main research interests, as long as I am able to provide a useful perspective in addressing them.
A summary of some work from 2017 can be found here.
TA: MT 2014-C5.7 Topics in Fluid Mechanics, HT 2015-MMSC B5.2 Applied Partial Differential Equations, MT 2015-MMSC Supplementary Applied Mathematics, HT 2016-MMSC Further Mathematical Methods
Departmental Tutor: MT 2016-C5.12 Mathematical Physiology
Pembroke Stipendiary Lectureship: MT 2017-Prelims Introductory Calculus, Part A Differential Equations I, HT 2018-Prelims Dynamics, Part A Differential Equations II, Waves and Fluids, Statistics, TT Part A Mathematical Biology
St. Anne's Stipendiary Lectureship: MT 2015-Prelims Introductory Calculus, Geometry, HT 2016-Part A Differential Equations 2, Integral Transforms
Major / Recent Publications:
- A. L. Krause, V. Klika, T. E. Woolley, and E. A. Gaffney. Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems. Physical Review E, 97:052206, 2018.
- A. L. Krause, L. Kurowski, K. Yawar, and R. A. Van Gorder. Stochastic Epidemic Metapopulation Models on Networks: SIS Dynamics and Control Strategies. Journal of Theoretical Biology, 449:35–52, 2018.
- A. L. Krause, A. M. Burton, N. T. Fadai, and R. A. Van Gorder. Emergent structures in reaction-advection-diffusion systems on a sphere. Physical Review E, 97:042215, 2018.
- A. L. Krause, D. Beliaev, R. A. Van Gorder, and S. L. Waters. Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media. International Journal of Bifurcation and Chaos, 2018. arXiv:1702.08345 [q-bio], In Press.
- A. L. Krause, D. Beliaev, R. A. Van Gorder, and S. L. Waters. Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold. IMA Mathematical Medicine and Biology, February 2018. arXiv:1702.07711 [q-bio], In Press.
- R. A. Van Gorder, A. L. Krause, F. Brosa Planella, and A. M. Burton. Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation. Annals of Physics, 2018. arXiv:1710.07968 [nlin.PS], In Press.
- R. M. Eide, A. L. Krause, N. T. Fadai, and R. A. Van Gorder. Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Journal of Theoretical Biology, 2018. In Press.
- J. A. Kwiecinski, A. Kovacs, A. L. Krause, F. Brosa Planella, and R. A. Van Gorder. Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations. International Journal of Bifurcation and Chaos, 2018. In Press.
- J. A. Kwiecinski, A. L. Krause, and R. A. Van Gorder. Effects of tidal torques on 1i/2017 U1 (‘Oumuamua). Icarus, 311:170 – 174, 2018.
- L. Kurowski, A. L. Krause, H. Mizuguchi, P. Grindrod, and R. A. Van Gorder, Two-Species Migration and Clustering in Two-Dimensional Domains. Bulletin of Mathematical Biology, 79(10), pp.2302-2333, 2017
A. Bassett, A. L. Krause, and R. A. Van Gorder, Continuous dispersal in a model of predator–prey-subsidy population dynamics. Ecological Modelling, 354, pp.115-122, 2017
A. Krause and B. Wang, Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains. Journal of Mathematical Analysis and Applications, 417(2), pp.1018-1038, 2014
- A. Krause, M. Lewis and B. Wang, Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative noise. Applied Mathematics and Computation, 246, pp.365-376, 2014.