Carlo Laing's Publications
Papers (Chronological)
Note: copyright is often held by the publisher.
- "Low-dimensional behaviour of nonlinear tearing mode dynamics in
a rotating plasma." M. Persson and C. Laing. Int. J. Bifn. Chaos. (vol.
3, pp. 1155-1168, 1993)
- "Successive homoclinic tangencies to a limit cycle." P. Hirschberg
and Carlo Laing. Physica D. (vol. 89, pp. 1-14, 1995). PDF version.
- "A homoclinic heirarchy." P. Glendinning and C. Laing, Physics
Letters A. (vol. 211, pp. 155-160, 1996). PDF version.
- "Bifocal homoclinic bifurcations." Carlo Laing and Paul Glendinning.
Physica D. (vol. 102, pp. 1-14, 1997). PDF version.
- "Rotating waves in rings of coupled oscillators." Carlo R.
Laing. Dynamics and Stability of Systems (vol. 13, no. 4, pp. 305-318, 1998). Gzipped postscript version. PDF version.
- "The postprocessed Galerkin method applied to nonlinear shell vibrations."
C. Laing, Allan McRobie and J. M. T. Thompson. Dynamics and Stability
of Systems (vol. 14, no. 2, pp. 163-181, 1999). Gzipped postscript
version.PDF version.
- "Symmetry and Chaos in the Complex Ginzburg-Landau Equation. I:
Reflectional symmetries." P. Aston and C. Laing. Dynamics and Stability
of Systems (vol. 14, no. 3, pp. 233-253, 1999). Gzipped postscript
text. PDF text. PDF whole paper.
- "Symmetry and Chaos in the Complex Ginzburg-Landau Equation. II:
Translational symmetries." P. Aston and C. Laing. Physica D (vol. 135,
pp. 79-97, 2000). Gzipped postscript text. PDF text. Full version, PDF.
- "Stationary bumps in networks of spiking neurons". Carlo Laing
and Carson Chow. Neural Computation (vol. 13, no. 7, pp. 1473-1494, 2001). Gzipped postscript version. PDF version.
- "Turning on and off with excitation: the role of spike-timing
asynchrony and synchrony in sustained neural activity". Gutkin, B.S.,
Laing, C.R., Colby, C.L., Chow, C.C., and Ermentrout, G.B. J. Computational
Neuroscience (vol 11, no. 2, pp. 121-134, 2001). PDF version. Gzipped postscript version.
- "Noise-induced stabilization of bumps in systems with long-range
spatial coupling". Carlo Laing and André Longtin. Physica D (vol
160, 3-4, pp. 149-172, 2001). Gzipped postscript version.PDF version.
- "Ghostbursting: a novel neuronal burst mechanism". Brent Doiron,
Carlo Laing, André Longtin and Len Maler. J. Computational Neuroscience
(vol 12, no. 1, pp. 5-25, 2002). PDF version, Gzipped postscript.
- "A spiking neuron model for binocular rivalry". Carlo Laing
and Carson Chow. J. Computational Neuroscience (vol 12, no. 1, pp. 39-53, 2002). PDF version. Gzipped postscript
version.
- "Multiple bumps in a neuronal model of working memory". Carlo
Laing, William Troy, Boris Gutkin and Bard Ermentrout. SIAM J. Appl. Math.
(Vol. 63, no. 1, pp. 62-97, 2002) Gzipped postscript. PDF.
- "Ghostbursting: the effects of dendrites on spike patterns". Carlo
Laing, Brent Doiron, André Longtin and Len Maler. Neurocomputing (vol
44-46, pp. 127-132, 2002). PDF.
- "A two-variable model of somatic-dendritic interactions in a bursting
neuron". Carlo Laing and André Longtin. Bull. Math. Biol. (vol
64, no. 5, pp. 829-860, 2002). Gzipped postscript. PDF.
- "A dynamic dendritic refractory period regulates burst discharge
in the electrosensory lobe of weakly electric fish." L. Noonan, B. Doiron,
C. R. Laing, A. Longtin and R. W. Turner. J. Neuroscience. (vol 23, no. 4,
pp. 1524-1534, 2003) PDF
- "Type I burst excitability." C. R. Laing, B. Doiron, A. Longtin,
L. Noonan, R. W. Turner and L. Maler. J. Comput. Neurosci. (vol. 14, no. 3,
pp. 329-342, 2003) Zipped version. PDF.
- "Two-bump solutions of Amari-type models of neuronal pattern formation."
Carlo Laing and William Troy. Physica D. (vol. 178, pp. 190-218, 2003).PDF. Zipped.
- "Periodic forcing of a model sensory neuron." C. R. Laing and
A. Longtin. Phys. Rev. E. (vol. 67, 051928, 2003). PDF.
Zipped version.
- "Dynamics of deterministic and stochastic paired excitatory-inhibitory
delayed feedback." C. R. Laing and A. Longtin. Neural Computation. (vol
15, no 12, pp. 2779-2822, 2003). PDF. Zipped
version.
- "PDE methods for non-local models." C. R. Laing and W. C. Troy.
SIAM J Appl Dyn Syst. (Vol 2, no. 3, pp. 487-516, 2003). PDF
(5.7 MB).
- "Ghostbursting in sensory cells of electric fish." C. R. Laing.
Invited article. Nonlinear Studies (vol 11, no. 3, pp. 469-480, 2004). Zipped
version. PDF.
- "Spiral Waves in Disinhibited Mammalian Neocortex" X. Huang, W. C. Troy, S. J. Schiff,
Q. Yang, H. Ma, C. R. Laing and J.-Y. Wu. J. Neuroscience. (Vol. 24, no 44, pp. 9897-9902, 2004)
PDF
- "Mode locking in a periodically forced "ghostbursting" neuron model."
C. R. Laing and S. Coombes. International Journal of Bifurcation
and Chaos. (Vol. 15, no. 4, pp. 1433-1444, 2005) PDF.
- "Spiral waves in nonlocal equations". C. R. Laing. SIAM J.
Appl. Dyn. Sys. (Vol 4, no. 3, pp. 588-606, 2005). PDF.
- "On the application of "equation-free" modelling to neural systems."
C. R. Laing. J. Comput. Neurosci. (Vol. 20, pp. 5-23, 2006).PDF.
Published version.
- "The importance of different timings of excitatory and inhibitory pathways in neural field models."
C. Laing and S. Coombes. Network: Computation in Neural Systems. (Vol. 17, No. 2, pp. 151-172, 2006).
PDF.
PDF as published.
- "Coarse-grained dynamics of an activity bump in a
neural field model."
C. R. Laing, T. A. Frewen and I. G. Kevrekidis. Nonlinearity (Vol. 20, pp. 2127-2146, 2007).
PDF.
- "Bumps, rings, and spots in a two-dimensional neural
field: splitting and rotational instabilities." M. R. Owen, C. R. Laing and S. Coombes.
New Journal of Physics. (Vol. 9, 378, 2007).
PDF.
- "Modeling electrocortical activity through improved local
approximations of integral neural field equations."
S. Coombes, N. A. Venkov, L. Shiau, I. Bojak, D. T. J. Liley and C. R. Laing.
Physical Review E. (Vol 76, 051901, 2007). PDF.
- "Periodically-forced finite networks of heterogeneous coupled oscillators:
a low-dimensional approach." C. R. Laing and I. G. Kevrekidis. Physica D (Vol. 237, pp. 207-215, 2008).
PDF.
- "Delays in activity based neural networks." S. Coombes and C. Laing. Philosophical
Transactions of the Royal Society A. (Vol. 367, pp. 1117-1129, 2009) PDF.
- "Instabilities in threshold-diffusion equations with delay" S. Coombes and C. R. Laing.
Physica D (Vol. 238, pp. 264-272, 2009).
PDF.
- "Transient Turing patterns in a neural field model" A. J. Elvin, C. R. Laing, and M. G. Roberts. Phys. Rev. E
(Vol. 79, 011911, 2009). PDF.
- "Chimera states in heterogeneous networks" C. R. Laing. Chaos (Vol. 19, 013113, 2009).
PDF.
- "The dynamics of chimera states in heterogeneous Kuramoto networks" C. R. Laing.
Physica D. (Vol. 238, pp. 1569-1588, 2009). PDF.
- "Exploiting the Hamiltonian structure of a neural field
model" A. J. Elvin, C. R. Laing, R. I. McLachlan and M. G. Roberts.
Physica D. (Vol. 239, pp. 537-546, 2010). PDF.
- "Solvable Model of Spiral Wave Chimeras"
E. A. Martens, C. R. Laing and S. H. Strogatz. Physical Review Letters (Vol. 104, 044101, 2010).
PDF. (Note that Fig. 4 here is slightly different from that in the published version.)
- "Reduced models for binocular rivalry."
C. R. Laing, T. Frewen and I. G. Kevrekidis. J. Comput. Neurosci. (Vol. 28, pp. 459-476, 2010).
PDF.
- "Chimeras in networks of planar oscillators"
C. R. Laing. Phys. Rev. E (Vol. 81, 066221, 2010).
PDF.
- "Bifurcations of smooth and lurching waves in
a one-dimensional thalamic neuronal network." T. M. Wasylenko, J. E. Cisternas, C. R. Laing and I. G.
Kevrekidis. Biological Cybernetics (Vol. 103, no. 6, pp. 447-462, 2010). PDF.
- "Pulsating fronts in periodically modulated neural field models" S. Coombes and C. R. Laing.
Phys. Rev. E. (Vol. 83, 011912, 2011).PDF.
- "Fronts and bumps in spatially extended Kuramoto networks" C. R. Laing.
Physica D, (Vol. 240, pp. 1960-1971, 2011). PDF.
- "Waves in random neural media." S. Coombes, H. Schmidt, C. R. Laing, N Svanstedt and
J. A. Wyller. Discrete and Continuous Dynamical Systems - Series A.
(vol. 32, pp. 2951-2970, 2012).
PDF.
- "Chimeras in random non-complete networks of phase oscillators." C. R. Laing,
K. Rajendran and I. G. Kevrekidis. Chaos, (vol. 22. 013132, 2012). PDF.
- "Managing heterogeneity in the study of neural oscillator dynamics."
C. R. Laing, Y. Zou, B. Smith and I. G. Kevrekidis. Journal of Mathematical Neuroscience.
(Vol. 2, number 5, 2012).
PDF.
- "Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks"
C. R. Laing. Chaos. (vol. 22. 043104, 2012). PDF.
- "Periodically forced piecewise linear adaptive exponential integrate-and-fire neuron"
L. Shiau and C. R. Laing. International Journal of Bifurcation
and Chaos. (vol. 23, 1350171, 2013). PDF.
- "Partially coherent twisted states in arrays of coupled phase oscillators"
O. Omel'chenko, M. Wolfrum, and C. R. Laing. Chaos, (vol. 24, 023102, 2014). PDF.
- "Numerical bifurcation theory for high-dimensional neural models"
Carlo R. Laing. Journal of Mathematical Neuroscience. (Vol. 4, number 13, 2014).
Link.
- "Derivation of a neural field model from a network of theta neurons"
Carlo R. Laing. Phys. Rev. E. (Vol. 90, 010901(R), 2014) PDF.
- "Coarse-grained clustering dynamics of synaptically coupled heterogeneous neurons"
Sung Joon Moon, Katherine A. Cook, K. Rajendran, Ioannis G. Kevrekidis, J. Cisternas and
Carlo R. Laing. Journal of Mathematical Neuroscience. (Vol. 5, number 2, 2015).
Link.
- "Exact neural fields incorporating gap junctions"
Carlo R. Laing. SIAM J. Applied Dynamical Systems. (Vol. 14, No. 4, pp. 1899–1929, 2015)
PDF.
- "Equation-free analysis of spike timing dependent plasticity"
Carlo R. Laing and Ioannis G. Kevrekidis. Biological Cybernetics. (Vol. 109, Issue 6, pp 701-714, 2015).
PDF.
- "Chimeras in networks with purely local coupling"
Carlo R. Laing. Phys. Rev. E. (Vol. 92, 050904(R), 2015) PDF.
- "Chimera states in networks of phase oscillators:
the case of two small populations"
Mark J. Panaggio, Daniel M. Abrams, Peter Ashwin and Carlo R. Laing. Phys. Rev. E.
(Vol. 93, 012218, 2016) PDF.
- "Exact analytical expressions for the final epidemic size of an SIR model on small networks"
Karen McCulloch, Mick G. Roberts and
Carlo R. Laing. The ANZIAM Journal. (Vol. 57, Issue 4, pp. 429-444, 2016).
Link.
- "Neural field models with threshold noise"
Ruediger Thul, Stephen Coombes and Carlo Laing. Journal of Mathematical Neuroscience.
(Vol. 6, number 3, 2016).
Link.
- "Travelling waves in arrays of delay-coupled phase oscillators"
Carlo R. Laing. Chaos. (Vol. 26, 094802, 2016) PDF.
- "Modeling Heterogeneity in Networks using Polynomial Chaos."
Karthikeyan Rajendran, Andreas C. Tsoumanis, Constantinos I. Siettos,
Carlo R. Laing, Ioannis G. Kevrekidis. International Journal for Multiscale Computational Engineering.
(Vol. 14, Issue 3, pp. 291–302, 2016)
PDF.
- "Bumps in small-world networks" Carlo R. Laing. Frontiers in Computational Neuroscience.
(Vol. 10, number 53, 2016). PDF.
Link to journal.
- "Dimension reduction in heterogeneous neural networks: generalized Polynomial
Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)" Minseok Choi, Tom Bertalan
Carlo R. Laing, Ioannis G. Kevrekidis. Eur. Phys. J. Special Topics (Vol. 225, pp. 1165–1180, 2016).
PDF.
- "Chimeras in two-dimensional domains: heterogeneity and the continuum limit"
Carlo R. Laing.
SIAM J. Applied Dynamical Systems. (Vol. 16, No. 2, pp. 974–1014, 2017) PDF.
- "Coarse-grained descriptions of dynamics for networks with both intrinsic and structural heterogeneities"
Tom Bertalan, Yan Wu, Carlo Laing, C. William Gear, Ioannis G. Kevrekidis.
Frontiers in Computational Neuroscience. (Vol. 11, number 43, 2017)
Link.
- "The dynamics of networks of identical theta
neurons"
Carlo R. Laing. Journal of Mathematical Neuroscience.
(Vol. 8, number 4, 2018).
Link.
- "Chaos in small networks of theta neurons"
Carlo R. Laing. Chaos. (Vol. 28, 073101, 2018) PDF.
Link.
- "Generalised probability mass function for the final epidemic size of an SIR model on a line of
triangles network"
Karen McCulloch, Carlo Laing, Mick Roberts. Mathematical Biosciences. (Vol. 311, pp. 49-61, 2019).
Link.
Unpublished
"Understanding the Dynamics of Biological and Neural Oscillator
Networks through Mean-Field Reductions: A Review"
Christian Bick, Marc Goodfellow, Carlo R. Laing, Erik Andreas Martens.
"Dynamics and stability of chimera states in two coupled populations
of oscillators"
Carlo R. Laing.
Books Edited
"Stochastic Methods in Neuroscience." Ed. C.
Laing and G. J. Lord. Publisher's page.
Popular articles
"Not so shocking: the electric fish of South America." C. R.
Laing, South American Explorer (vol 69, 2002). Postscript.
PDF.
"Taking the pulse" C. R.
Laing, Physics (vol 7, 2014). link
Book chapters
"Phase oscillator network models of brain dynamics"
C. R. Laing, in
"Computational Models of Brain and Behavior"
Edited by Ahmed Moustafa (Wiley-Blackwell, 2017). PDF
"Waves in spatially-disordered neural fields: a case study in uncertainty quantification."
C. R. Laing, in "Uncertainty in Biology:
a computational modeling approach."
Edited by Liesbet Geris and David Gomez-Cabrero (Springer-Verlag, 2015). PDF
"PDE Methods for Two-Dimensional Neural
Fields". C. R. Laing,
in "Neural Fields"
ed. Stephen Coombes,
Peter beim Graben,
Roland Potthast, and
James J. Wright. (Springer, 2014).
PDF
"Correlations and memory in neurodynamical systems". A. Longtin,
C. R. Laing and M. J. Chacron, in "Processes with Long Range Correlations".
Edited by G. Rangarajan and M. Ding. (Springer-Verlag, Berlin, 2003). PDF. Compressed postscript.
"Ghostbursting: the role of active dendrites in electrosensory
processing". C. R. Laing
and B. Doiron, in "Bursting:
The Genesis of Rhythm in the Nervous
System", ed. S. Coombes and P. Bressloff
(World Scientific). PDF.
Book reviews
"Mathematical Biology. I: an introduction". by J. D. Murray.
Reviewed for NZ Math Society Newsletter, no. 87 (April 2003).
"Mathematical Biology. II: spatial models and biomedical applications".
by J. D. Murray.
Reviewed for NZ Math Society Newsletter, no. 90 (April 2004).
"Mathematics handbook for science and engineering".
by L. Rade and B. Westergren.
Reviewed for NZ Math Society Newsletter, no. 93 (April 2005).
Theses
"Merging of Resonance Tongues near the Saddle-node/Hopf Bifurcation."
M.Sc. (Physics) Thesis. University of Auckland, 1994.
Postscript summary of my PhD thesis, "Coupled
Oscillator Networks" , University of Cambridge, 1997.
Carlo's homepage