Carlo Laing's Publications

Papers (Chronological)
Note: copyright is often held by the publisher.  
  1. "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)
  2. "Successive homoclinic tangencies to a limit cycle." P. Hirschberg and Carlo Laing. Physica D. (vol. 89, pp. 1-14, 1995). PDF version.
  3. "A homoclinic heirarchy." P. Glendinning and C. Laing, Physics Letters A. (vol. 211, pp. 155-160, 1996). PDF version.
  4. "Bifocal homoclinic bifurcations." Carlo Laing and Paul Glendinning. Physica D. (vol. 102, pp. 1-14, 1997). PDF version.
  5. "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.
  6. "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.
  7. "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.
  8. "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.
  9. "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.
  10.  "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.
  11. "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.
  12. "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.
  13. "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.
  14. "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.
  15. "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.
  16. "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.
  17. "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
  18. "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.
  19. "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.
  20. "Periodic forcing of a model sensory neuron." C. R. Laing and A. Longtin. Phys. Rev. E. (vol. 67, 051928, 2003). PDF. Zipped version.
  21. "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.
  22. "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).
  23. "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.
  24. "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
  25. "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.
  26. "Spiral waves in nonlocal equations". C. R. Laing. SIAM J. Appl. Dyn. Sys. (Vol 4, no. 3, pp. 588-606, 2005). PDF.
  27. "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.
  28. "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.
  29. "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.
  30. "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.
  31. "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.
  32. "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.
  33. "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.
  34. "Instabilities in threshold-diffusion equations with delay" S. Coombes and C. R. Laing. Physica D (Vol. 238, pp. 264-272, 2009). PDF.
  35. "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.
  36. "Chimera states in heterogeneous networks" C. R. Laing. Chaos (Vol. 19, 013113, 2009). PDF.
  37. "The dynamics of chimera states in heterogeneous Kuramoto networks" C. R. Laing. Physica D. (Vol. 238, pp. 1569-1588, 2009). PDF.
  38. "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.
  39. "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.)
  40. "Reduced models for binocular rivalry." C. R. Laing, T. Frewen and I. G. Kevrekidis. J. Comput. Neurosci. (Vol. 28, pp. 459-476, 2010). PDF.
  41. "Chimeras in networks of planar oscillators" C. R. Laing. Phys. Rev. E (Vol. 81, 066221, 2010). PDF.
  42. "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.
  43. "Pulsating fronts in periodically modulated neural field models" S. Coombes and C. R. Laing. Phys. Rev. E. (Vol. 83, 011912, 2011).PDF.
  44. "Fronts and bumps in spatially extended Kuramoto networks" C. R. Laing. Physica D, (Vol. 240, pp. 1960-1971, 2011). PDF.
  45. "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.
  46. "Chimeras in random non-complete networks of phase oscillators." C. R. Laing, K. Rajendran and I. G. Kevrekidis. Chaos, (vol. 22. 013132, 2012). PDF.
  47. "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.
  48. "Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks" C. R. Laing. Chaos. (vol. 22. 043104, 2012). PDF.
  49. "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.
  50. "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.
  51. "Numerical bifurcation theory for high-dimensional neural models" Carlo R. Laing. Journal of Mathematical Neuroscience. (Vol. 4, number 13, 2014). Link.
  52. "Derivation of a neural field model from a network of theta neurons" Carlo R. Laing. Phys. Rev. E. (Vol. 90, 010901(R), 2014) PDF.
  53. "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.
  54. "Exact neural fields incorporating gap junctions" Carlo R. Laing. SIAM J. Applied Dynamical Systems. (Vol. 14, No. 4, pp. 1899–1929, 2015) PDF.
  55. "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.
  56. "Chimeras in networks with purely local coupling" Carlo R. Laing. Phys. Rev. E. (Vol. 92, 050904(R), 2015) PDF.
  57. "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.
  58. "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.
  59. "Neural field models with threshold noise" Ruediger Thul, Stephen Coombes and Carlo Laing. Journal of Mathematical Neuroscience. (Vol. 6, number 3, 2016). Link.
  60. "Travelling waves in arrays of delay-coupled phase oscillators" Carlo R. Laing. Chaos. (Vol. 26, 094802, 2016) PDF.
  61. "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.
  62. "Bumps in small-world networks" Carlo R. Laing. Frontiers in Computational Neuroscience. (Vol. 10, number 53, 2016). PDF. Link to journal.
  63. "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.
  64. "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.
  65. "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.
  66. "The dynamics of networks of identical theta neurons" Carlo R. Laing. Journal of Mathematical Neuroscience. (Vol. 8, number 4, 2018). Link.
  67. "Chaos in small networks of theta neurons" Carlo R. Laing. Chaos. (Vol. 28, 073101, 2018) PDF. Link.
  68. "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.
  69. "Dynamics and stability of chimera states in two coupled populations of oscillators" Carlo R. Laing. Phys. Rev. E. (Vol. 100, 042211, 2019). PDF.
  70. "The effects of within-neuron degree correlations in networks of spiking neurons" Carlo R. Laing and Christian Blasche. Biological Cybernetics. (Vol. 114, pp. 337-347, 2020) PDF. Link.
  71. "Degree assortativity in networks of spiking neurons" Christian Blasche, Shawn Means, and Carlo R. Laing. Journal of Computational Dynamics. (Vol. 7, no. 2, pp. 401-423, 2020) PDF Link.
  72. "Emergent spaces for coupled oscillators " Thomas N. Thiem, Mahdi Kooshkbaghi, Tom Bertalan, Carlo R. Laing , and Ioannis G. Kevrekidis. Frontiers in Computational Neuroscience. (Vol. 14, 36, 2020). Link.
  73. "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. Journal of Mathematical Neuroscience. (Vol. 10, Article number: 9 (2020)) Link.
  74. "Moving bumps in theta neuron networks" Carlo R. Laing and Oleh Omel'chenko. Chaos (Vol. 30, 043117, 2020). PDF.
  75. "A permutation method for network assembly" Shawn Means, Christian Blasche, and Carlo R. Laing. PLoS ONE, 15(10): e0240888, 2020. Link
  76. "Dynamics of structured networks of Winfree oscillators." Carlo R. Laing, Christian Blasche and Shawn Means. Frontiers in Systems Neuroscience (Vol. 15, art. 631377, 2021). Link
  77. "Effects of degree distributions in random networks of Type-I neurons." Carlo R. Laing. Phys. Rev. E. (Vol. 103, 052305, 2021) PDF.
  78. "Global and Local Reduced Models for Interacting, Heterogeneous Agents." Thomas N. Thiem, Felix P. Kemeth, Tom Bertalan, Carlo R. Laing, and Ioannis G. Kevrekidis. Chaos (Vol. 31, 073139, 2021). Link
  79. "Interpolating between bumps and chimeras" Carlo R. Laing. Chaos (Vol. 31, 113116, 2021). PDF
  80. "Collective states in a ring network of theta neurons." Oleh Omel'chenko and Carlo R. Laing. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2259), 2022. PDF
  81. "Chimeras with uniformly distributed heterogeneity: Two coupled populations." Carlo R. Laing. Physical Review E (Vol. 105, 024306, 2022). PDF
  82. "Explosive behaviour in networks of Winfree oscillators." Shawn Means and Carlo R. Laing. Chaos, Solitons and Fractals, (Vol. 160, 112254, 2022). PDF
  83. "Learning emergent PDEs in a learned emergent space." Felix P. Kemeth, Tom Bertalan, Thomas Thiem, Felix Dietrich, Sung Joon Moon, Carlo R. Laing and Ioannis G. Kevrekidis. Nature Communications, (Vol. 13, 3318, 2022). Article
  84. "Chimeras on annuli." Carlo R. Laing. Chaos (Vol. 32, 083105, 2022). PDF
  85. "Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing." Carlo R. Laing and Bernd Krauskopf. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2266), 2022. PDF Link
  86. "Chimeras on a ring of oscillator populations" Carlo R. Laing. Chaos (Vol. 33, 013121, 2023). PDF
  87. "Periodic solutions in next generation neural field models" Carlo R. Laing and Oleh Omel'chenko. Biological Cybenetics (Vol. 117, 259–274, 2023). PDF Link to journal
  88. "Chimeras in phase oscillator networks locally coupled through an auxiliary field: stability and bifurcations" Carlo R. Laing. Chaos (Vol. 33, 083141, 2023). PDF
  89. "Ion channels and the diversity of spontaneous firing in anterior pituitary corticotrophs: A dynamical analysis" Jian Song, Carlo R. Laing, Shenquan Liu. Communications in Nonlinear Science and Numerical Simulation (Vol. 131, 107789, 2024). Link to journal
  90. "Activity patterns in ring networks of quadratic integrate-and-fire neurons with synaptic and gap junction coupling" Oleh Omel'chenko and Carlo R. Laing. Phys. Rev. E. (Vol. 110, 034411, 2024) PDF

Unpublished

  • "Periodic solutions for a pair of delay-coupled active theta neurons" Carlo R. Laing. To appear in The ANZIAM Journal, 2024. PDF
  • "Subsystem Resetting of a Heterogeneous Network of Theta Neurons" Na Zhao, Carlo R. Laing, Jian Song and Shenquan Liu. Submitted 2024.
  • "Periodic solutions for a pair of delay-coupled excitable theta neurons" Bernd Krauskopf and Carlo R. Laing. Submitted 2024.
    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