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.

Preprints/Submitted Papers

P4. E. A. Gaffney, A. L. Krause, P. K. Maini, and C. Wang. Spatial Heterogeneity Localizes Turing Patterns in Reaction-Cross-Diffusion Systems. arXiv preprint

P3. A. L. Krause, E. A. Gaffney, and B. J. Walker. Concentration-dependent domain evolution in reaction-diffusion systems. arXiv preprint

P2. J. Glover, Z. Sudderick, L. Charlton, B. Shih, C. Batho-Samblas, A. L. Krause, C. Anderson, J. Riddell, A. Balic, J. Li, V. Klika, T. Woolley, E. A. Gaffney, A. Corsinotti, R. Anderson, S. Wang, Y. Chen, M. Crichton, and D. Headon. The developmental basis of fingerprint pattern formation and variation. Available on request.

P1. A. Sadier, N. Anthwal, A. L. Krause, R. Dessalles, M. Lake, L. Bentolila, R. Haase, N. Nieves, S. Santana, and K. E. Sears. Growth rate as a modulator of tooth patterning during adaptive radiations. bioRxiv preprint

Journal Articles

35. J. S. Ritchie, A. L. Krause, and R. A. Van Gorder. Turing and wave instabilities in hyperbolic reaction-diffusion systems: the role of second-order time derivatives and cross-diffusion terms on pattern formation. Annals of Physics, 444:169033, 2022. Preprint (arXiv), Journal

34. A. Sargood, E. A. Gaffney, and A. L. Krause. Fixed and distributed gene expression time delays in reaction-diffusion systems. Bulletin of Mathematical Biology, 83, 98, 2022. Preprint (arXiv), Journal (Open Access)

33. A. L. Krause, E. A. Gaffney, P. K. Maini, and V. Klika. Modern perspectives on near-equilibrium analysis ofTuring systems. Philosophical Transactions of the Royal Society A, 379(2213):20200268, 2021. Preprint (arXiv), Journal (Open Access)

32. A. L. Krause, E. A. Gaffney, P. K. Maini, and V Klika. Introduction to 'Recent Progress and Open Frontiers in Turing’s Theory of Morphogenesis’. Philosophical Transactions of the Royal Society A, 379(2213):20200280, 2021. Journal (Open Access)

31. A. L. Krause, V. Klika, P. K. Maini, D. Headon, and E. A. Gaffney. Isolating Patterns in Open Reaction-Diffusion Systems. Bulletin of Mathematical Biology, 83(7):1–35, 2021. Preprint (arXiv), Journal (Open Access)

30. R. A. Van Gorder, A. Kamilova, and A. L. Krause. Locating the baking isotherm in a Søderberg electrode: analysis of a moving thermistor model. SIAM Journal on Applied Mathematics, 2021, 81(4):1691–1716, 2021. Preprint (ORA), Journal

29. T. E. Woolley, A. L. Krause, and E. A. Gaffney. Bespoke Turing Systems. Bulletin of Mathematical Biology, 83(41):1–32, 2021. Journal (Open Access)

28. R. A. Van Gorder, V. Klika, and A. L. Krause. Turing conditions for pattern forming systems on evolving manifolds. Journal of Mathematical Biology, 2020. 82:4. Preprint (arXiv), Journal

27. A. L. Krause, V. Klika, J. Halatek, P K. Grant, T. E. Woolley, N. Dalchau, and E. A. Gaffney. Turing patterning in stratified domains, Bulletin of Mathematical Biology, 2020. 82:136. Preprint (arXiv), Journal

26. A. L. Krause and R. A. Van Gorder. A non-local cross-diffusion model of population dynamics II: exact, approximate, and numerical traveling waves in single- and multi-species populations. Bulletin of Mathematical Biology, 82:113, 2020. Preprint (ORA), Journal

25. N. P. Taylor, H. Kim, A. L. Krause, and R. A. Van Gorder. A non-local cross-diffusion model of population dynamics I: Emergent spatial and spatiotemporal patterns. Bulletin of Mathematical Biology, 82:112, 2020. Preprint (ORA), Journal

24. J. C. Price, A. L. Krause, S.L. Waters, and A. J. El Haj. Predicting bone formation in MSC seeded hydrogels using experiment based mathematical modelling. Tissue Engineering Part A, 26(17–18):1014–1023, 2020. Preprint (ORA), Journal

23. R. A. Van Gorder, A. L. Krause, B. A. Malomed, and D. J. Kaup. Unstaggered-staggered solitons on one-and two-dimensional two-component discrete nonlinear Schrödinger lattices. Communications in Nonlinear Science and Numerical Simulation, 2020. 85:105244, 2020. Preprint (arXiv), Journal

22. 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, 17:20190621, 2020. Preprint (arXiv), Journal

21. 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 cancer invasion. Bulletin of Mathematical Biology, 82:15 , 2020. Preprint (bioRxiv), Journal

20. 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. Preprint (ORA), Journal

19. 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. Preprint (ORA), Journal

18. 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. Preprint (ORA), Journal

17. 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. Preprint (ORA), Journal

16. 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. Preprint (arXiv), Journal

15. 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. Preprint (ORA), Journal

14. 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. Preprint (arXiv), Journal

13. 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. Preprint (ORA), Journal

12. 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. Preprint (ORA), Journal

11. 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. Preprint (ORA), Journal

10 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. Preprint (arXiv), Journal

9. 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. Preprint (ORA), Journal

8. 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. Preprint (ORA), Journal

7. 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. Preprint (ORA), Journal

6. 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. Preprint (arXiv), Journal

5. 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. Preprint (ORA), Journal

4. 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. Preprint (ORA), Journal

3. 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. Preprint (ORA), Journal

2. 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. Journal

1. 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. Preprint (arXiv), Journal

Edited Issues

Recent Progress and Open Frontiers in Turing’s Theory of Morphogenesis, Theme Issue of the Philosophical Transactions of the Royal Society A. Guest edited Theme Issue with Vaclav Klika, Eamonn Gaffney, and Philip Maini. Introductory Article, Blog Post

Theses

2. A. L. Krause. Network Modelling of Bioactive Porous Media. DPhil Thesis, University of Oxford, 2017. ORA

1. A. Krause. Asymptotic Dynamics of Stochastic p-Laplace Equations on Unbounded Domains. Msc Thesis, New Mexico Tech, 2014. arXiv