Professor Georg Gottwald

F07 - Carslaw Building
The University of Sydney

Telephone 9351 5784
Fax 9351 4534

Website Personal Webpage
Curriculum vitae Curriculum vitae

Research interests

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.

Teaching and supervision

Timetable

Editorial work:

  • Associate Editor for Geophysical and Astrophysical Fluid Dynamics
  • 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" (2014)

International links

United Kingdom

(University of Surrey) Visiting Professor

Selected grants

2015

  • Detection and Generation of Anomalous Diffusion: A Dynamical Systems Approach; Melbourne I, Gottwald G; DVC Research/International Research Collaboration Award (IRCA).

2012

  • Extracting macroscopic variables and their dynamics in multiscale systems with metastable states; Gottwald G, Froyland G; Australian Research Council (ARC)/Discovery Projects (DP).

2010

  • Stochastic Methods in Mathematical Geophysical Fluid Dynamics; Gottwald G; Australian Research Council (ARC)/Future Fellowships (FT).

2006

  • Nonlinear Time Series Analysis in Cardiac Physiology; Gottwald G; Australian Research Council (ARC)/Discovery Projects (DP).

2004

  • Geometric methods in geophysical fluid dynamics; Gottwald G; Australian Research Council (ARC)/Discovery Projects (DP).
  • Complex Open Systems Network (COSNet); Cairns I, Robinson P, Gottwald G, et a, Dewar R; Australian Research Council (ARC)/Research Networks (ARCRN).

Selected publications

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Journals

  • Gottwald, G., Melbourne, I. (2014). A test for a conjecture on the nature of attractors for smooth dynamical system. Chaos, 24, 024403-1-024403-9.
  • Gottwald, G. (2014). Controlling balance in an ensemble Kalman filter. Nonlinear Processes in Geophysics, 21, 417-426. [More Information]
  • Maclean, J., Gottwald, G. (2014). On convergence of the projective integration method for stiff ordinary differential equations. Communications in Mathematical Sciences, 14(2), 235-255. [More Information]
  • Gottwald, G., Skokos, C. (2014). Preface to the Focus Issue: Chaos Detection Methods and Predictability. Chaos, 24, 024201-1-024201-2.
  • Gottwald, G., Oliver, M. (2014). Slow dynamics via degenerate variational asymptotics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 470, 20140460.
  • Gottwald, G., Melbourne, I. (2013). A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proceedings of the National Academy of Sciences (PNAS) 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. Royal Meteorological Society. Quarterly Journal, 139(670), 212-225. [More Information]
  • Gottwald, G., Melbourne, I. (2013). Homogenization for deterministic maps and multiplicative noise. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 469(2156), 1-17. [More Information]
  • Frank, J., Gottwald, G. (2013). Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere. Physica D: Nonlinear Phenomena, 254, 46-56. [More Information]
  • Gottwald, G., Harlim, J. (2013). The role of additive and multiplicative noise in filtering complex dynamical systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 469(2155), 1-16. [More Information]
  • 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]
  • 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]
  • 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]
  • Gottwald, G., Oliver, M. (2009). Boltzmann's Dilemma: An Introduction to Statistical Mechanics via the Kac Ring. SIAM Review, 51(3), 613-635.
  • Bergemann, K., Gottwald, G., Reich, S. (2009). Ensemble propagation and continuous matrix factorization algorithms. Royal Meteorological Society. Quarterly Journal, 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.
  • Menon, S., Gottwald, G. (2009). On bifurcations in a chaotically stirred excitable medium. Physica D: Nonlinear Phenomena, 238(4), 461-475.
  • Gottwald, G., Melbourne, I. (2009). On the implementation of the 0-1 test for chaos. SIAM Journal on Applied Dynamical Systems, 8(1), 129-145.
  • Gottwald, G., Melbourne, I. (2009). On the validity of the 0-1 test for chaos. Nonlinearity, 22(6), 1367-1382.
  • Gottwald, G. (2008). Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? Chaos: an interdisciplinary journal of nonlinear science, 18(1), 013129-1-013129-17.
  • Gottwald, G., Melbourne, I. (2008). Comment on "Reliability of the 0 - 1 test for chaos". Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 77(2), 028201-1-028201-2.
  • Melbourne, I., Gottwald, G. (2008). Power spectra for deterministic chaotic dynamical systems. Nonlinearity, 21(1), 179-189.
  • Dritschel, D., Scott, R., Macaskill, C., Gottwald, G., Tran, C. (2008). Unifying Scaling Theory for Vortex Dynamics in Two-Dimensional Turbulence. Physical Review Letters, 101, 094501-1-094501-4.
  • 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.
  • Menon, S., Gottwald, G. (2007). Bifurcations of flame filaments in chaotically mixed combustion reactions. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 75(1), 016209-1-016209-13.
  • 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]
  • Balasuriya, S., Gottwald, G., Hornibrook, J., Lafortune, S. (2007). High Lewis number combustion wavefronts: a perturbative Melnikov analysis. SIAM Journal on Applied Mathematics, 67(2), 464-486.
  • Gottwald, G., Oliver, M., Tecu, N. (2007). Long time accuracy for approximate slow manifolds in a finite-dimensional model of balance. Journal of Nonlinear Science, 17(4), 283-307. [More Information]
  • Cox, S., Gottwald, G. (2006). A bistable reaction-diffusion system in a stretching flow. Physica D: Nonlinear Phenomena, 216(2), 307-318.
  • Gottwald, G., Kramer, L. (2006). A normal form for excitable media. Chaos: an interdisciplinary journal of nonlinear science, 16(013122), 1-10.
  • Thuraisingham, R., Gottwald, G. (2006). On multiscale entropy analysis for physiological data. Physica A: Statistical Mechanics and its Applications, 366(1), 323-332.
  • 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.
  • Menon, S., Gottwald, G. (2005). Bifurcations in reaction-diffusion systems in chaotic flows. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 71(6), 066201-1-066201-7.
  • Gottwald, G., Melbourne, I. (2005). Testing for chaos in deterministic systems with noise. Physica D: Nonlinear Phenomena, 212(1-2), 100-110.
  • Gottwald, G., Melbourne, I. (2004). A New Test For Chaos In Deterministic Systems. Proceedings of the Royal Society of London. Mathematical, Physical and Engineering Sciences, 460(2042), 603-611.
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14.
  • Gottwald, G., Kramer, L. (2004). On Propagation Failure In One- And Two-Dimensional Excitable Media. Chaos: an interdisciplinary journal of nonlinear science, 14(3), 855-863.
  • 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.
  • 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: Statistical Mechanics and its Applications, 303(3-4), 387-396.
  • Grimshaw, R., Malomed, B., Gottwald, G. (2002). Singular and regular gap solitons between three dispersion curves. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 65(6), 066606-1-066606-14.
  • Bridges, T., Derks, G., Gottwald, G. (2002). Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework. Physica D: Nonlinear Phenomena, 172(1-4), 190-216.
  • 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: an interdisciplinary journal of nonlinear science, 11(3), 487-494.

2014

  • Gottwald, G., Melbourne, I. (2014). A test for a conjecture on the nature of attractors for smooth dynamical system. Chaos, 24, 024403-1-024403-9.
  • Gottwald, G. (2014). Controlling balance in an ensemble Kalman filter. Nonlinear Processes in Geophysics, 21, 417-426. [More Information]
  • Maclean, J., Gottwald, G. (2014). On convergence of the projective integration method for stiff ordinary differential equations. Communications in Mathematical Sciences, 14(2), 235-255. [More Information]
  • Gottwald, G., Skokos, C. (2014). Preface to the Focus Issue: Chaos Detection Methods and Predictability. Chaos, 24, 024201-1-024201-2.
  • Gottwald, G., Oliver, M. (2014). Slow dynamics via degenerate variational asymptotics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 470, 20140460.

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 (PNAS) 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. Royal Meteorological Society. Quarterly Journal, 139(670), 212-225. [More Information]
  • Gottwald, G., Melbourne, I. (2013). Homogenization for deterministic maps and multiplicative noise. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 469(2156), 1-17. [More Information]
  • Frank, J., Gottwald, G. (2013). Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere. Physica D: Nonlinear Phenomena, 254, 46-56. [More Information]
  • Gottwald, G., Harlim, J. (2013). The role of additive and multiplicative noise in filtering complex dynamical systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 469(2155), 1-16. [More Information]

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.
  • Bergemann, K., Gottwald, G., Reich, S. (2009). Ensemble propagation and continuous matrix factorization algorithms. Royal Meteorological Society. Quarterly Journal, 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.
  • Menon, S., Gottwald, G. (2009). On bifurcations in a chaotically stirred excitable medium. Physica D: Nonlinear Phenomena, 238(4), 461-475.
  • Gottwald, G., Melbourne, I. (2009). On the implementation of the 0-1 test for chaos. SIAM Journal on Applied Dynamical Systems, 8(1), 129-145.
  • Gottwald, G., Melbourne, I. (2009). On the validity of the 0-1 test for chaos. Nonlinearity, 22(6), 1367-1382.

2008

  • Gottwald, G. (2008). Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? Chaos: an interdisciplinary journal of nonlinear science, 18(1), 013129-1-013129-17.
  • Gottwald, G., Melbourne, I. (2008). Comment on "Reliability of the 0 - 1 test for chaos". Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 77(2), 028201-1-028201-2.
  • Melbourne, I., Gottwald, G. (2008). Power spectra for deterministic chaotic dynamical systems. Nonlinearity, 21(1), 179-189.
  • Dritschel, D., Scott, R., Macaskill, C., Gottwald, G., Tran, C. (2008). Unifying Scaling Theory for Vortex Dynamics in Two-Dimensional Turbulence. Physical Review Letters, 101, 094501-1-094501-4.

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.
  • Menon, S., Gottwald, G. (2007). Bifurcations of flame filaments in chaotically mixed combustion reactions. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 75(1), 016209-1-016209-13.
  • 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]
  • Balasuriya, S., Gottwald, G., Hornibrook, J., Lafortune, S. (2007). High Lewis number combustion wavefronts: a perturbative Melnikov analysis. SIAM Journal on Applied Mathematics, 67(2), 464-486.
  • Gottwald, G., Oliver, M., Tecu, N. (2007). Long time accuracy for approximate slow manifolds in a finite-dimensional model of balance. Journal of Nonlinear Science, 17(4), 283-307. [More Information]

2006

  • Cox, S., Gottwald, G. (2006). A bistable reaction-diffusion system in a stretching flow. Physica D: Nonlinear Phenomena, 216(2), 307-318.
  • Gottwald, G., Kramer, L. (2006). A normal form for excitable media. Chaos: an interdisciplinary journal of nonlinear science, 16(013122), 1-10.
  • Thuraisingham, R., Gottwald, G. (2006). On multiscale entropy analysis for physiological data. Physica A: Statistical Mechanics and its Applications, 366(1), 323-332.

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.
  • Menon, S., Gottwald, G. (2005). Bifurcations in reaction-diffusion systems in chaotic flows. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 71(6), 066201-1-066201-7.
  • Gottwald, G., Melbourne, I. (2005). Testing for chaos in deterministic systems with noise. Physica D: Nonlinear Phenomena, 212(1-2), 100-110.

2004

  • Gottwald, G., Melbourne, I. (2004). A New Test For Chaos In Deterministic Systems. Proceedings of the Royal Society of London. Mathematical, Physical and Engineering Sciences, 460(2042), 603-611.
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14.
  • Gottwald, G., Kramer, L. (2004). On Propagation Failure In One- And Two-Dimensional Excitable Media. Chaos: an interdisciplinary journal of nonlinear science, 14(3), 855-863.

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.

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: Statistical Mechanics and its Applications, 303(3-4), 387-396.
  • Grimshaw, R., Malomed, B., Gottwald, G. (2002). Singular and regular gap solitons between three dispersion curves. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 65(6), 066606-1-066606-14.
  • Bridges, T., Derks, G., Gottwald, G. (2002). Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework. Physica D: Nonlinear Phenomena, 172(1-4), 190-216.

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: an interdisciplinary journal of nonlinear science, 11(3), 487-494.

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