People_
Professor Georg Gottwald
Professor in the School of Mathematics and Statistics
I work in dynamical systems. Dynamical systems theory is an active and exciting area of modern mathematics which provides an abstract formalism for studying systems evolving in time and/or space. It is a powerful tool to unveil general and universal mechanisms underpinning the plethora of dynamical behaviors observed in nature. This allows us to apply those ideas in constructive ways to understand and control dynamical systems in nature and technology, with applications ranging from biology to weather and climate.
Timetable
(University of Surrey) Visiting Professor |
Project title | Research student |
---|---|
Physics-informed machine intelligence with neuromorphic nano-systems. | Yinhao XU |
Selected publications
Publications
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Edited Books
- Skokos, C., Gottwald, G., Laskar, J. (2016). Chaos Detection and Predictability. Berlin: Springer-Verlag. [More Information]
Book Chapters
- Gottwald, G., Crommelin, D., Franzke, C. (2017). Stochastic Climate Theory. In Christian L E Franzke, Terence J OKane (Eds.), Nonlinear and Stochastic Climate Dynamics, (pp. 209-240). Cambridge: Cambridge University Press. [More Information]
- Gottwald, G., Melbourne, I. (2016). The 0-1 Test for Chaos: A Review. In Charalampos Skokos, Georg A Gottwald, Jacques Laskar (Eds.), Chaos Detection and Predictability, (pp. 221-247). Berlin: Springer-Verlag. [More Information]
Journals
- Yue, W., Gottwald, G. (2024). A stochastic approximation for the finite-size Kuramoto–Sakaguchi model. Physica D: Nonlinear Phenomena, 468(November 2024), 134292-1-134292-15. [More Information]
- Engel, M., Gottwald, G. (2024). Canards in modified equations for Euler discretizations. Contemporary Mathematics, 806, 15-28. [More Information]
- Riechers, K., Gottwald, G., Boers, N. (2024). Glacial Abrupt Climate Change as a Multiscale Phenomenon Resulting from Monostable Excitable Dynamics. Journal of Climate, 37(8), 2741-2763. [More Information]
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2024
- Yue, W., Gottwald, G. (2024). A stochastic approximation for the finite-size Kuramoto–Sakaguchi model. Physica D: Nonlinear Phenomena, 468(November 2024), 134292-1-134292-15. [More Information]
- Engel, M., Gottwald, G. (2024). Canards in modified equations for Euler discretizations. Contemporary Mathematics, 806, 15-28. [More Information]
- Riechers, K., Gottwald, G., Boers, N. (2024). Glacial Abrupt Climate Change as a Multiscale Phenomenon Resulting from Monostable Excitable Dynamics. Journal of Climate, 37(8), 2741-2763. [More Information]
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2023
- Fialkowski, J., Yanchuk, S., Sokolov, I., Scholl, E., Gottwald, G., Berner, R. (2023). Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks. Physical Review Letters, 130(6), Article 067402-1-Article 067402-7. [More Information]
- Jiao, C., Gottwald, G. (2023). Levy flights as an emergent phenomenon in a spatially extended system. Proceedings of the Royal Society A, 479, 20230349-1-20230349-16. [More Information]
- Sandoz, A., Ducret, V., Gottwald, G., Vilmart, G., Perron, K. (2023). SINDy for delay-differential equations: application to model bacterial zinc response. Proceedings of the Royal Society A, 479 Open Access(2269), 20220556 -1-20220556 - 18. [More Information]
2022
- James, N., Menzies, M., Gottwald, G. (2022). On financial market correlation structures and diversification benefits across and within equity sectors. Physica A, 604, Article 127682 - 1-Article 127682 - 18. [More Information]
2021
- Gottwald, G. (2021). A model for Dansgaard–Oeschger events and millennial-scale abrupt climate change without external forcing. Climate Dynamics, 56(1-2), 227-243. [More Information]
- Cartwright, M., Gottwald, G. (2021). Collective coordinate framework to study solitary waves in stochastically perturbed Korteweg–de Vries equations. Physical Review E, 104, 024201 - 1-024201 - 13. [More Information]
- Gottwald, G., Reich, S. (2021). Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations. Chaos, 31(10), 101103. [More Information]
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2020
- Gottwald, G., Gugole, F. (2020). Detecting Regime Transitions in Time Series Using Dynamic Mode Decomposition. Journal of Statistical Physics, 179, 1028-1045. [More Information]
- Gottwald, G. (2020). Introduction to Focus Issue: Linear response theory: Potentials and limits. Chaos, 30, 020401 - 1-02401 - 3. [More Information]
- Smith, L., Gottwald, G. (2020). Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit. Chaos, 30(9), 093107-1-093107-12. [More Information]
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2019
- Cartwright, M., Gottwald, G. (2019). A collective coordinate framework to study the dynamics of travelling waves in stochastic partial differential equations. Physica D: Nonlinear Phenomena, 397, 54-64. [More Information]
- Wohltmann, I., Lehmann, R., Gottwald, G., Peters, K., Protat, A., Louf, V., Williams, C., Feng, W., Rex, M. (2019). A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts (LaConTra v1.0). Geoscientific Model Development, 12(10), 4387-4407. [More Information]
- Smith, L., Gottwald, G. (2019). Chaos in networks of coupled oscillators with multimodal natural frequency distributions. Chaos, 29(9), 093127-1-093127-17. [More Information]
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2018
- Frank, J., Gottwald, G. (2018). A note on statistical consistency of numerical integrators for multiscale dynamics. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 16(2), 1017-1033. [More Information]
- Balasuriya, S., Gottwald, G. (2018). Estimating stable and unstable sets and their role as transport barriers in stochastic flows. Physical Review E, 98, 013106-1-013106-17. [More Information]
- Hancock, E., Gottwald, G. (2018). Model reduction for Kuramoto models with complex topologies. Physical Review E, 98, 012307-1-012307-9. [More Information]
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2017
- Dritschel, D., Gottwald, G., Oliver, M. (2017). Comparison of variational balance models for the rotating shallow water equations. Journal of Fluid Mechanics, 822, 689-716. [More Information]
- Gottwald, G. (2017). Finite-size effects in a stochastic Kuramoto model. Chaos, 27(10), 101103-1-101103-6. [More Information]
- Gottwald, G., Mohamad, H., Oliver, M. (2017). Optimal Balance via Adiabatic Invariance of Approximate Slow Manifolds. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 15(4), 1404-1422. [More Information]
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2016
- Gottwald, G., Peters, K., Davies, L. (2016). A data-driven method for the stochastic parametrisation of subgrid-scale tropical convective area fraction. Quarterly Journal of the Royal Meteorological Society, 142, 349-359. [More Information]
- Froyland, G., Gottwald, G., Hammerlindl, A. (2016). A trajectory-free framework for analysing multiscale systems. Physica D: Nonlinear Phenomena, 328-329, 34-43. [More Information]
- Gottwald, G., Melbourne, I. (2016). Broadband nature of power spectra for intermittent maps with summable and nonsummable decay of correlations. Journal of Physics A: Mathematical and Theoretical, 49(March 2016), 174003-17 pages. [More Information]
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2015
- Gottwald, G. (2015). Model reduction for networks of coupled oscillators. Chaos, 25, 1-12. [More Information]
- Maclean, J., Gottwald, G. (2015). On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations. Journal of Computational and Applied Mathematics, 288, 44-69. [More Information]
2014
- Froyland, G., Gottwald, G., Hammerlindl, A. (2014). A computational method to extract macroscopic variables and their dynamics in multi-scale systems. SIAM Journal on Applied Dynamical Systems, 13(4), 1816-1846. [More Information]
- Gottwald, G., Melbourne, I. (2014). A test for a conjecture on the nature of attractors for smooth dynamical system. Chaos, 24(2), 1-9. [More Information]
- Gottwald, G. (2014). Controlling balance in an ensemble Kalman filter. Nonlinear Processes in Geophysics, 21(2), 417-426. [More Information]
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2013
- Gottwald, G., Melbourne, I. (2013). A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proceedings of the National Academy of Sciences of the United States of America, 110(21), 8411-8416. [More Information]
- Gottwald, G., Majda, A. (2013). A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks. Nonlinear Processes in Geophysics, 20, 705-712. [More Information]
- Mitchell, L., Gottwald, G. (2013). Controlling model error of underdamped forecast models in sparse observational networks using a variance-limiting Kalman filter. Quarterly Journal of the Royal Meteorological Society, 139(670), 212-225. [More Information]
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2012
- Mitchell, L., Gottwald, G. (2012). Data assimilation in slow-fast systems using homogenized climate models. Journal of the Atmospheric Sciences, 69(4), 1359-1377. [More Information]
- Mitchell, L., Gottwald, G. (2012). On finite-size Lyapunov exponents in multiscale systems. Chaos, 22(2), 023115-1-023115-9. [More Information]
2011
- Gottwald, G., Mitchell, L., Reich, S. (2011). Controlling Overestimation of Error Covariance in Ensemble Kalman Filters with Sparse Observations: A Variance-Limiting Kalman Filter. Monthly Weather Review, 139, 2650-2667. [More Information]
- Kelly, D., Gottwald, G. (2011). On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators. Chaos, 21(2), 025110-1-025110-10. [More Information]
- Frank, J., Gottwald, G. (2011). The Langevin Limit of the Nosé-Hoover-Langevin Thermostat. Journal of Statistical Physics, 143(4), 715-724. [More Information]
2010
- Gottwald, G. (2010). On recent trends in climate dynamics. Gazette of the Australian Mathematical Society, 37(5), 319-326.
- Hermann, S., Gottwald, G. (2010). The large core limit of spiral waves in excitable media: a numerical approach. SIAM Journal on Applied Dynamical Systems, 9(2), 536-567. [More Information]
- Balasuriya, S., Gottwald, G. (2010). Wavespeed in reaction-diffusion systems, with applications to chemotaxis and population pressure. Journal of Mathematical Biology, 61(3), 377-399. [More Information]
2009
- Gottwald, G., Oliver, M. (2009). Boltzmann's Dilemma: An Introduction to Statistical Mechanics via the Kac Ring. SIAM Review, 51(3), 613-635. [More Information]
- Bergemann, K., Gottwald, G., Reich, S. (2009). Ensemble propagation and continuous matrix factorization algorithms. Quarterly Journal of the Royal Meteorological Society, 135(643), 1560-1572. [More Information]
- Dritschel, D., Scott, R., Macaskill, C., Gottwald, G., Tran, C. (2009). Late time evolution of unforced inviscid two-dimensional turbulence. Journal of Fluid Mechanics, 640, 215-233. [More Information]
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2008
- Gottwald, G. (2008). Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? Chaos, 18(1), 013129-1-013129-17. [More Information]
- Gottwald, G., Melbourne, I. (2008). Comment on "Reliability of the 0 - 1 test for chaos". Physical Review E, 77(2), 028201-1-028201-2. [More Information]
- Melbourne, I., Gottwald, G. (2008). Power spectra for deterministic chaotic dynamical systems. Nonlinearity, 21(1), 179-189. [More Information]
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2007
- Falconer, I., Gottwald, G., Melbourne, I., Wormnes, K. (2007). Application of the 0-1 Test for Chaos to Experimental Data. SIAM Journal on Applied Dynamical Systems, 6(2), 395-402. [More Information]
- Menon, S., Gottwald, G. (2007). Bifurcations of flame filaments in chaotically mixed combustion reactions. Physical Review E, 75(1), 016209-1-016209-13. [More Information]
- Gottwald, G. (2007). Dispersive regularizations and numerical discretizations for the inviscid Burgers equation. Journal of Physics A: Mathematical and Theoretical, 40(49), 14745-14758. [More Information]
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2006
- Cox, S., Gottwald, G. (2006). A bistable reaction-diffusion system in a stretching flow. Physica D: Nonlinear Phenomena, 216(2), 307-318. [More Information]
- Gottwald, G., Kramer, L. (2006). A normal form for excitable media. Chaos, 16(013122), 1-10. [More Information]
- Thuraisingham, R., Gottwald, G. (2006). On multiscale entropy analysis for physiological data. Physica A, 366(1), 323-332. [More Information]
2005
- Derks, G., Gottwald, G. (2005). A robust numerical method to study oscillatory instability of gap solitary waves. SIAM Journal on Applied Dynamical Systems, 4(1), 140-158. [More Information]
- Menon, S., Gottwald, G. (2005). Bifurcations in reaction-diffusion systems in chaotic flows. Physical Review E, 71(6), 066201-1-066201-7. [More Information]
- Gottwald, G., Melbourne, I. (2005). Testing for chaos in deterministic systems with noise. Physica D: Nonlinear Phenomena, 212(1-2), 100-110. [More Information]
2004
- Gottwald, G., Melbourne, I. (2004). A New Test For Chaos In Deterministic Systems. Proceedings of the Royal Society A, 460(2042), 603-611. [More Information]
- Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14. [More Information]
- Gottwald, G., Kramer, L. (2004). On Propagation Failure In One- And Two-Dimensional Excitable Media. Chaos, 14(3), 855-863. [More Information]
2003
- Dullin, H., Gottwald, G., Holm, D. (2003). Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves. Fluid Dynamics Research, 33(1), 73-95. [More Information]
2002
- Frank, J., Gottwald, G., Reich, S. (2002). A Hamiltonian particle-mesh method for the rotating shallow water equations. Lecture Notes in Computational Science and Engineering, 26, 131-142.
- Gottwald, G., Nicol, M. (2002). On the nature of Benford’s Law. Physica A, 303(3-4), 387-396.
- Grimshaw, R., Malomed, B., Gottwald, G. (2002). Singular and regular gap solitons between three dispersion curves. Physical Review E, 65(6), 066606-1-066606-14. [More Information]
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2001
- Dullin, H., Gottwald, G., Holm, D. (2001). An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion. Physical Review Letters, 87(19), 4501-4504.
- Gottwald, G., Pumir, A., Krinsky, V. (2001). Spiral wave drift induced by stimulating wave trains. Chaos, 11(3), 487-494.
Selected Grants
2022
- A dynamical systems theory approach to machine learning, Gottwald G, Australian Research Council (ARC)/Discovery Projects (DP)
2018
- Mathematical model reduction for complex networks, Gottwald G, Australian Research Council (ARC)/Discovery Projects (DP)
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Editorial work:
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Advisory Board for Chaos
href="http://aip.scitation.org/journal/cha">Chaos: An Interdisciplinary Journal of Nonlinear Sciencehref="http://aip.scitation.org/journal/cha">Chaos: An Interdisciplinary Journal of Nonlinear Science
- Associate Editor for Geophysical and Astrophysical Fluid Dynamics
- Editor for Chaos Focus Issue on "Linear Response Theory: Potentials and Limits" (2020)
- Editor for Chaos Focus Issue on "Chaos Prediction Methods and Predictability" (2014)
- Editor for Springer Lecture Notes in Physics on "Chaos Prediction Methods and Predictability" (2016)
- Associate Editor forSIAM Journal of Applied Dynamical Systems
- Editorial Board forPhysical Review E
- Associate EditorforJournal of Computational Dynamics