Research & Publications

Google Scholar Profile, CV

I am broadly interested in mathematical biology as well as nonlinear dynamical systems with applications to other areas of science. I am particularly interested in understanding and overcoming the limits of current methodologies to capture spatial and temporal complexity in phenomena 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, with 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 areas I am interested both in the scientific field or application, as well as in the theoretical and 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 problems 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. In short, I am problem-driven rather than technique-constrained.


  1. R. A. Van Gorder, V. Klika, and A. L. Krause. Turing conditions for pattern forming systems on evolving manifolds. arXiv:1904.09683 [nlin.PS].

Journal Articles

  1. A. L. Krause, V. Klika, T. E. Woolley, and E. A. Gaffney. From one pattern into another: Analysis of Turing patterns in heterogeneous domains via WKBJ. Journal of the Royal Society Interface, in Press arXiv:1908.07219 [nlin.PS].
  2. M. A. R. Strobl, A. L. Krause, M. Damaghi, R. Gillies, A. R. A. Anderson, and P. K. Maini. Mix & match: Phenotypic coexistence as a key facilitator of solid tumour invasion. Bulletin of Mathematical Biology, in Press. bioRxiv
  3. Y. Xu, A. L. Krause, and R. A. Van Gorder. Generalist predator dynamics under Kolmogorov versus non-Kolmogorov models. Journal of Theoretical Biology, 486:110060, 2020.
  4. A. L. Krause, M. Ellis, and R. A. Van Gorder. Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds. Bulletin of Mathematical Biology, 81(3):1–41, 2019.
  5. R. A. Van Gorder, H. Kim, and A. L. Krause. Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains. Journal of Fluid Mechanics, 877:759–823, 2019.
  6. E. F. Fussell, A. L. Krause, and R. A. Van Gorder. Hybrid approach to modeling spatial dynamics of systems with generalist predators. Journal of Theoretical Biology, 462:26–47, 2019.
  7. R. A. Van Gorder, A. L. Krause, and J. A. Kwiecinski. Amplitude death criteria for coupled complex Ginzburg-Landau systems. Nonlinear Dynamics, 97:151–159, 2019.
  8. F. Sánchez-Garduño, A. L. Krause, J. A. Castillo, and P. Padilla. Turing–Hopf patterns on growing domains: the torus and the sphere. Journal of Theoretical Biology, 481:136–150, 2019.
  9. 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, 36(3):325–360, 2019.
  10. 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.
  11. 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.
  12. 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.
  13. 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, 28(11):1830037, 2018.
  14. V. Klika and A. L. Krause. Beyond Onsager-Casimir relations: Shared dependence of phenomenological coefficients on state variables. The Journal of Physical Chemistry Letters, 9:7021–7025, 2018.
  15. 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, 396:397–428, 2018
  16. 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, 451:19–34, 2018.
  17. 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, 28(05):1830013, 2018.
  18. 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.
  19. 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
  20. 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
  21. 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
  22. 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.