Publications

Preprints

G.A. Gottwald, F. Li, Y. Marzouk and S. Reich
Stable generative modelling using diffusion maps
W. Yue and G.A. Gottwald
A stochastic approximation for the finite-size Kuramoto-Sakaguchi model
L. Smith and G.A. Gottwald
Data assimilation for networks of coupled oscillators: Inferring unknown model parameters from partial observations
G.A. Gottwald and I. Melbourne
Time-reversibility and nonvanishing Lévy area

Selected Review Articles

G.A. Gottwald, D. Crommelin and C. Franzke
Stochastic climate theory
In Nonlinear and Stochastic Climate Dynamics, Cambridge University Press (C. Franzke and T. O'Kane, eds.) (2017) DOI
G.A. Gottwald and I. Melbourne
The 0-1 test for chaos: A review
In Chaos Detection and Predictability, Springer Lecture Notes in Physics 915 (C. Skokos, G.A. Gottwald and J. Laskar, eds.) (2016) DOI

Peer-Reviewed Journal Articles

K. Riechers, N. Boers and G.A. Gottwald
Glacial abrupt climate change as a multi-scale phenomenon resulting from monostable excitable dynamics
Journal of Climate 37(8) (2024) 2741-2763. DOI
C. Jiao and G.A. Gottwald
Lévy flights as an emergent phenomenon in a spatially extended system
Proc. Roy. Soc. A 479 (2023) 20230349. DOI
M. Engel and G.A. Gottwald
Canards in modified equations for Euler discretizations
accepted in AMS Contemporary Mathematics (2023)
J. Fialkowski, S. Yanchuk, I. Sokolov, E. Schöll, G.A. Gottwald and R. Berner
Heterogeneous nucleation in finite size adaptive dynamical networks
Phys. Rev. Lett. 130 (2023) 067402. DOI
A. Sandoz, V. Ducret, G.A. Gottwald, G. Vilmart and K. Perron
SINDy for delay-differential equations: application to model bacterial zinc response
Proc. Roy. Soc. A 479 (2023) 20220556. DOI A figure from this paper was chosen as the journal cover image.
N. James, M. Menzies and G.A. Gottwald
On financial market correlation structures and diversification benefits across and within equity sectors
Physica A 604 (2022) 127682. DOI
G.A. Gottwald and S. Reich
Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
Chaos 31 (2021) 101103. DOI This paper was selected as Featured and as a Scilight
M. Cartwright and G.A. Gottwald
A collective coordinate framework to study solitary waves in stochastically perturbed Korteweg-de Vries equations
Phys. Rev. E 104 (2021) 024201. DOI
L. Smith and G.A. Gottwald
Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
Chaos 31 (2021) 073116. DOI
G.A. Gottwald and S. Reich
Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation
Physica D 423 (2021) 132911. DOI
G.A. Gottwald and I. Melbourne
Simulation of non-Lipschitz stochastic differential equations driven by α-stable noise: a method based on deterministic homogenisation
SIAM MMS 19 (2021) 665-687. DOI
G.A. Gottwald
A model for Dansgaard-Oeschger events and millennial-scale abrupt climate change without external forcing
Climate Dynamics 56 (2021) 227-243. DOI
L. Smith and G.A. Gottwald
Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit
Chaos 30 (2020) 093107. DOI
B. Giggins and G.A. Gottwald
Stochastically perturbed bred vectors in single-scale systems
Q.J.R. Meteorolog. Soc. 146(733) (2020) 4038-4054. DOI
W. Yue, L. Smith and G.A. Gottwald
Model reduction for the Kuramoto-Sakaguchi model: The importance of non-entrained rogue oscillators
Phys. Rev. E 101 (2020) 062213. DOI
G.A. Gottwald and F. Gugole
Detecting regime transitions using dynamic mode decomposition
J. Stat. Phys. 179 (2020) 1028-1045. DOI
C. Wormell and G.A. Gottwald
Linear response for macroscopic observables in high-dimensional systems
Chaos 29 (2019) 113127. This paper was chosen as an Editor's pick. DOI
I. Wohltmann, R. Lehmann, G.A. Gottwald, K. Peters, A. Protat, V. Louf, C. Williams, W. Feng and M. Rex
A Lagrangian convective transport scheme including a simulation of the time air parcels spend in updrafts
Geoscientific Model Development 12 (2019) 4387-4407. DOI
J. Wouters and G.A. Gottwald
Stochastic model reduction for slow-fast systems with moderate time-scale separation
SIAM MMS 17(4) (2019) 1172-1188. DOI
L. Smith and G.A. Gottwald
Chaos in networks of coupled oscillators with multimodal frequency distributions
Chaos 29 (2019) 093127. DOI
M. Cartwright and G.A. Gottwald
A collective coordinate framework to study the dynamics of travelling waves in stochastic partial differential equations
Physica D 397 (2019) 54-64. DOI
J. Wouters and G.A. Gottwald
Edgeworth expansions for slow-fast systems with finite time scale separation
Proc. Roy. Soc. A 475 (2019) 20180358. DOI
B. Giggins and G.A. Gottwald
Stochastically perturbed bred vectors in multi-scale systems
Q.J.R. Meteorolog. Soc. 145(719) (2019) 642-658. DOI
G.A. Gottwald and D.E. Pelinovsky
On the impossibility of solitary Rossby waves in meridionally unbounded domains
Physics of Fluids 30 (2018) 116601. DOI
S. Balasuriya and G.A. Gottwald
On estimating stochastic stable and unstable sets and their role as transport barriers in stochastic flows
Phys. Rev. E 98 (2018) 013106. DOI
E.J. Hancock and G.A. Gottwald
Model reduction for Kuramoto models with complex topologies
Phys. Rev. E 98 (2018) 012307. DOI
C. Wormell and G.A. Gottwald
On the validity of linear response theory in high-dimensional deterministic dynamical systems
J. Stat. Phys. 172 (2018) 1479-1498. DOI
J. Frank and G.A. Gottwald
A note on statistical consistency of numerical integrators for multi-scale dynamics
SIAM MMS 16(2) (2018) 1017-1033. DOI
G.A. Gottwald
Finite-size effects in a stochastic Kuramoto model
Chaos 27 (2017) 101103. DOI
C.J. Cotter, G.A. Gottwald and D.D. Holm
Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
Proc. Roy. Soc. A 473 (2017) 20170388. DOI
G.A. Gottwald, H. Mohamad and M. Oliver
Optimal balance via adiabatic invariance of approximate slow manifolds
SIAM MMS 15(4) (2017) 1404-1422. DOI
D. Dritschel, G.A. Gottwald and M. Oliver
Comparison of variational balance models for the rotating shallow water equations
Journal of Fluid Mechanics 822 (2017) 689-716. DOI
G.A. Gottwald and I. Melbourne
On the detection of superdiffusive behaviour in time series
J. Stat. Mech. 2016 (12) (2016) 123205. DOI
G.A. Gottwald and I. Melbourne
Central limit theorems and suppression of anomalous diffusion for systems with symmetry
Nonlinearity 29 (2016) 2941-2960. DOI
G.A. Gottwald, J.P. Wormell and J. Wouters
On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series
Physica D 331 (2016) 89-101. DOI
G. Froyland, G.A. Gottwald and A. Hammerlindl
A trajectory-free framework for analysing multiscale systems
Physica D 328-329 (2016) 34-43. DOI
G.A. Gottwald and I. Melbourne
Broadband nature of power spectra for intermittent maps with summable and nonsummable decay of correlations
Journal of Physics A 49 (2016) 174003. This paper was chosen as a 2016 Highlight article. DOI
G.A. Gottwald, K. Peters and L. Davies
A data-driven method for the stochastic parametrisation of subgrid-scale tropical convective area fraction
Q.J.R. Meteorolog. Soc. 142 (2016) 349-359. DOI
G.A. Gottwald
Model reduction for networks of coupled oscillators
Chaos 25 (2015) 053111. DOI
J. Maclean and G.A. Gottwald
On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations
Journal of Computational and Applied Mathematics 288 (2015) 44-69. DOI

G. Froyland, G.A. Gottwald and A. Hammerlindl
A computational method to extract macroscopic variables and their dynamics in multi-scale systems
SIAM Journal on Applied Dynamical Systems 13(4) (2014) 1816-1846. DOI
G.A. Gottwald and M. Oliver
Slow dynamics via degenerate variational asymptotics
Proc. Roy. Soc. A 470 (2014) 20140460. DOI
G.A. Gottwald and I. Melbourne
A test for a conjecture on the nature of attractors for smooth dynamical systems
Chaos 24 (2014) 024403. DOI
G.A. Gottwald
Controlling balance in an Ensemble Kalman filter
Nonlin. Processes Geophys. 21 (2014) 417-426. DOI
J. Maclean and G.A. Gottwald
On convergence of the projective integration method for stiff ordinary differential equations
Comm. Math. Sci. 12(2) (2014) 235-255. DOI

G.A. Gottwald and A.J. Majda
A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks
Nonlin. Processes Geophys. 20 (2013) 705-712. DOI
G.A. Gottwald and I. Melbourne
Homogenization for deterministic maps and multiplicative noise
Proc. Roy. Soc. A 469 (2013) 20130201. DOI
corrected version, April 2015
G.A. Gottwald and I. Melbourne
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416. DOI
G.A. Gottwald and J. Harlim
The role of additive and multiplicative noise in filtering complex dynamical systems
(with Appendix)
Proc. Roy. Soc. A 469 (2013) 20130096. DOI
J. Frank and G.A. Gottwald
Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere
Physica D 254 (2013) 45-65. DOI
L. Mitchell and G.A. Gottwald
Controlling model error of underdamped forecast models in sparse observational networks using a variance limiting Kalman filter
Q.J.R. Meteorolog. Soc. 139 (2013) 212-225. DOI

L. Mitchell and G.A. Gottwald
On finite size Lyapunov exponents in multiscale systems
Chaos 22 (2012) 023115. DOI
L. Mitchell and G.A. Gottwald
Data assimilation in slow-fast systems using homogenized climate models
J. Atmos. Sci. 69 (2012) 1359-1377. DOI

J. Frank and G.A. Gottwald
The Langevin equation limit of the Nosé-Hoover-Langevin thermostat
J. Stat. Phys. 143 (2011) 715-724. DOI
D. Kelly and G.A. Gottwald
On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators
Chaos 21 (2011) 025110. DOI
G.A. Gottwald, L. Mitchell and S. Reich
Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter
Monthly Weather Review 139 (2011) 2650-2667. DOI

S. Hermann and G.A. Gottwald
The large core limit of spiral waves in excitable media: A numerical approach
SIAM Journal on Applied Dynamical Systems 9 (2010) 536-567. DOI
S. Balasuriya and G.A. Gottwald
Wavespeed in reaction-diffusion systems, with applications to chemotaxis and population pressure
J. Math. Biolog. 61 (2010) 377-399. DOI

D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
Late time evolution of unforced inviscid two-dimensional turbulence
Journal of Fluid Mechanics 640 (2009) 217-235. DOI
K. Bergemann, G.A. Gottwald and S. Reich
Ensemble propagation and continuous matrix factorization algorithms
Q.J.R. Meteorolog. Soc. 135 (2009) 1560-1572. DOI
G.A. Gottwald and I. Melbourne
On the validity of the 0-1 test for chaos
Nonlinearity 22 (2009) 1367-1382. DOI
G.A. Gottwald and M. Oliver
Boltzmann's dilemma -- an introduction to statistical mechanics via the Kac ring
SIAM Review 51 (2009) 613-635. DOI
S. Menon and G.A. Gottwald
On bifurcations in a chaotically stirred excitable medium
Physica D 238 (2009) 461-475. DOI
G.A. Gottwald and I. Melbourne
On the implementation of the 0-1 test for chaos
SIAM Journal on Applied Dynamical Systems 8 (2009) 129-145. DOI

D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
Unifying scaling theory for vortex dynamics in two-dimensional turbulence
Phys. Rev. Lett. 101 (2008) 094501. This paper was chosen as an Editor's Suggestion. DOI
G.A. Gottwald
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
Chaos 18 (2008) 013129. DOI
G.A. Gottwald and I. Melbourne
Comment on "Reliability of the 0-1 test for chaos"
Phys. Rev. E 77 (2008) 028201. DOI
G.A. Gottwald and I. Melbourne
Power spectra for deterministic chaotic dynamical systems
Nonlinearity 21 (2008) 179-189. This paper was chosen as a 2008 High-Profile article. DOI

G.A. Gottwald
Dispersive regularizations and numerical discretizations for the inviscid Burgers equation
J. Phys. A 40 (2007) 14745-14758. DOI
S. Menon and G.A. Gottwald
Bifurcations of flame filaments in chaotically mixed combustion reactions
Phys. Rev. E 75 (2007) 016209. DOI
S. Balasuriya, G.A. Gottwald, J. Hornibrook and S. Lafortune
High Lewis number combustion wavefronts: A perturbative Melnikov analysis
SIAM J. Applied Math. 67 (2007) 464-486. DOI
G.A. Gottwald, M. Oliver and N. Tecu
Long-time accuracy for approximate slow manifolds in a finite dimensional model of balance
Journal of Nonlinear Science 17 (2007) 383-307. DOI
I. Falconer, G.A. Gottwald, I. Melbourne and K. Wormnes
Application of the 0-1 test for chaos to experimental data
SIAM Journal on Applied Dynamical Systems 6 (2007) 395-402. DOI

G.A. Gottwald and L. Kramer
A normalform for excitable media
Chaos 16 (2006) 013122. DOI
S. Cox and G.A. Gottwald
A bistable reaction--diffusion system in a stretching flow
Physica D 216 (2006) 307-318. DOI
R.A. Thuraisingham and G.A. Gottwald
On multiscale entropy analysis for physiological data
Physica A 366 (2006) 323-332. DOI

S. Menon and G.A. Gottwald
Bifurcations in reaction-diffusion systems in chaotic flows
Phys. Rev. E 71 (2005) 066201. DOI
G.A. Gottwald and I. Melbourne
Testing for chaos in deterministic systems with noise
Physica D 212 (2005) 100-110. DOI
G. Derks and G.A. Gottwald
A robust numerical method to study oscillatory instability of gap solitary waves
SIAM Journal on Applied Dynamical Systems 4 (2005) 140-158. DOI

H.R. Dullin, G.A. Gottwald and D.D. Holm
On asymptotically equivalent shallow water wave equations
Physica D 190 (2004) 1-14. DOI
G.A. Gottwald and L. Kramer
Propagation failure in one- and two-dimensional excitable media
Chaos 14 (2004) 855-863. DOI
G.A. Gottwald and I. Melbourne
A new test for chaos in deterministic systems
Proc. Roy. Soc. Lond. A 460 (2004) 603-611. DOI

H.R. Dullin, G.A. Gottwald and D.D. Holm
Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves
Fluid Dynamics Research 33 (2003) 73-95. DOI

J. Frank, G.A. Gottwald and S. Reich
A Hamiltonian particle-mesh method for the rotating shallow-water equations
Meshless Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering ( M. Griebel and M.A. Schweitzer, eds.), Springer, 26 (2002) 131-142.
R.H.J. Grimshaw, B. Malomed and G.A. Gottwald
Singular and regular gap solitons between three dispersion curves
Phys. Rev. E 65 (2002) 066606. DOI
G.A. Gottwald and M. Nicol
On the nature of Benford's Law
Physica A 303 (2002) 387-396. DOI
T. Bridges, G. Derks, G.A. Gottwald
Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
Physica D 172 (2002) 190-216. DOI

H.R. Dullin, G.A. Gottwald and D.D. Holm
An integrable shallow water system with linear and nonlinear dispersion
Phys. Rev. Lett. 87 (2001) 194501. DOI
G.A. Gottwald, A. Pumir and V. Krinsky
Spiral wave drift induced by stimulating wave trains
Chaos 11 (2001) 487-494. DOI

G.A. Gottwald, L. Kramer, V. Krinsky, A. Pumir and V. Barelko
Persistence of zero velocity fronts in reaction diffusion systems
Chaos 10 (2000) 731-737. DOI

G.A. Gottwald and R.H.J. Grimshaw
The effect of topography on the dynamics of interacting solitary waves as an example for atmospheric blocking
J. Atmos. Sci. 56 (1999) 3663-3678. DOI
G.A. Gottwald and R.H.J. Grimshaw
The formation of coherent structures in the context of blocking
J. Atmos. Sci. 56 (1999) 3640-3662. DOI

G.A. Gottwald, R.H.J. Grimshaw and B. Malomed
Stable two-dimensional parametric solitons in hydrodynamic models
Phys. Lett. A 248 (1998) 208-218. DOI

G.A. Gottwald, R.H.J. Grimshaw and B. Malomed
Parametric envelope solitons in coupled Korteweg-de Vries equations
Phys. Lett. A 227 (1997) 47-54. DOI

Conference Proceedings and Other Publications

G.A. Gottwald
Introduction to Focus Issue: Linear response theory: Potentials and limits
Chaos 30 (2020) 020401. DOI
G.A. Gottwald and C. Skokos
Preface to the Focus Issue: Chaos Detection Methods and Predictability
Chaos 24 (2014) 024201. DOI
G.A. Gottwald, A. Majda, L. Mitchell and S. Reich
Constraining overestimation of error covariances in ensemble Kalman filters
In: Oberwolfach Reports, Volume 9, Issue 4, (2012). DOI
G.A. Gottwald
On recent trends in climate dynamics
Gazette of the Australian Mathematical Society 37 (5) (2010) 319-326.
D.G. Dritschel, R.K. Scott, C. Macaskill, G.A. Gottwald and C.V. Tran
Vortex self-similarity and the evolution of unforced inviscid two-dimensional turbulence
Advances in Turbulence XII, Springer Proceedings in Physics 132 (2009) 461-464. DOI
G.A. Gottwald and L. Kramer
On a normalform for excitable media
In: Oberwolfach Reports, Volume 2, Issue 3, (2005) 1941-1942. DOI
R.H.J. Grimshaw, B. Malomed and G.A. Gottwald
Cuspons and peakons vis-a-vis regular solitons and collapse in a three-wave system
In: Proceedings of the AMS-IMS-SIAM Conference "The Legacy of Inverse Scattering Theory in Nonlinear Wave Propagation" (J. Bona, R. Choudhury and D. Kaup, eds.). CONM (Contemporary Math) AMS series (2002). DOI
R.H.J. Grimshaw and G.A. Gottwald
Models for instability in geophysical flows
In: Proceedings of IUTAM Symposium on Advances in Mathematical Modelling of Atmosphere and Ocean Dynamics, (P.F. Hodnett, ed.), Kluwer Academic Publishers (2001) 153-161.
G.A. Gottwald, L. Kramer, V. Krinsky, A. Pumir and V. Barelko
Co-existence of stable states in reaction diffusion systems
In: Proceedings of "La 3ème Rencontre du Non-linéaire 2000", (Y. Pomeau and R. Ribotta, eds.), Orsay (2001) 154-158.