105
Views
53
CrossRef citations to date
0
Altmetric
Original Article

Pattern formation in intracortical neuronal fields

, &
Pages 351-368 | Received 25 Oct 2002, Published online: 09 Jul 2009

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (2)

N. P. Rougier & A. Hutt. (2011) Synchronous and asynchronous evaluation of dynamic neural fields. Journal of Difference Equations and Applications 17:8, pages 1119-1133.
Read now
Carlo Laing & Stephen Coombes. (2006) The importance of different timings of excitatory and inhibitory pathways in neural field models. Network: Computation in Neural Systems 17:2, pages 151-172.
Read now

Articles from other publishers (51)

Chih-Wen ShihJui-Pin TsengChang-Hong Wu. (2023) Absolute Stability and Synchronization in Second-Order Neural Fields with Conduction Delays. SIAM Journal on Applied Dynamical Systems 22:2, pages 878-917.
Crossref
Katharina Glomb, Joana Cabral, Anna Cattani, Alberto Mazzoni, Ashish Raj & Benedetta Franceschiello. (2021) Computational Models in Electroencephalography. Brain Topography 35:1, pages 142-161.
Crossref
Axel Hutt. 2022. Encyclopedia of Computational Neuroscience. Encyclopedia of Computational Neuroscience 2623 2628 .
Stephan van Gils & Wim van Drongelen. 2022. Encyclopedia of Computational Neuroscience. Encyclopedia of Computational Neuroscience 1330 1344 .
Forwah Amstrong Tah, Conrad Bertrand Tabi & Timoléon Crépin Kofane. (2021) Pattern formation in the Fitzhugh–Nagumo neuron with diffusion relaxation. Chaos, Solitons & Fractals 147, pages 110974.
Crossref
Conor L. Morrison, Priscilla E. Greenwood & Lawrence M. Ward. (2021) Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model. Physical Review E 103:3.
Crossref
Len Spek, Yuri A. Kuznetsov & Stephan A. van Gils. (2020) Neural field models with transmission delays and diffusion. The Journal of Mathematical Neuroscience 10:1.
Crossref
Johanna Senk, Karolína Korvasová, Jannis Schuecker, Espen Hagen, Tom Tetzlaff, Markus Diesmann & Moritz Helias. (2020) Conditions for wave trains in spiking neural networks. Physical Review Research 2:2.
Crossref
Sedaghat Shahmorad, M.H. Ostadzad & D. Baleanu. (2020) A Tau–like numerical method for solving fractional delay integro–differential equations. Applied Numerical Mathematics 151, pages 322-336.
Crossref
James Ross, Michelle Margetts, Ingo Bojak, Rachel Nicks, Daniele Avitabile & Stephen Coombes. (2020) Brain-wave equation incorporating axodendritic connectivity. Physical Review E 101:2.
Crossref
Peter H. Baxendale, Priscilla E. Greenwood & Lawrence M. Ward. (2019) Noise sharing and Mexican-hat coupling in a stochastic neural field. Physical Review E 100:2.
Crossref
Moira L. Steyn-Ross, D. A. Steyn-Ross, L. J. Voss & J. W. Sleigh. (2019) Spinodal decomposition in a mean-field model of the cortex: Emergence of hexagonally symmetric activation patterns. Physical Review E 99:1.
Crossref
Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy & Axel Hutt. (2018) Kernel Reconstruction for Delayed Neural Field Equations. The Journal of Mathematical Neuroscience 8:1.
Crossref
Axel Hutt, John D. Griffiths, Christoph S. Herrmann & Jérémie Lefebvre. (2018) Effect of Stimulation Waveform on the Non-linear Entrainment of Cortical Alpha Oscillations. Frontiers in Neuroscience 12.
Crossref
Grégory Faye & Zachary P. Kilpatrick. (2018) Threshold of Front Propagation in Neural Fields: An Interface Dynamics Approach. SIAM Journal on Applied Mathematics 78:5, pages 2575-2596.
Crossref
Jérémie Lefebvre, Axel Hutt & Flavio Frohlich. (2017) Stochastic resonance mediates the state-dependent effect of periodic stimulation on cortical alpha oscillations. eLife 6.
Crossref
Meysam Hashemi, Axel Hutt, Darren Hight & Jamie Sleigh. (2017) Anesthetic action on the transmission delay between cortex and thalamus explains the beta-buzz observed under propofol anesthesia. PLOS ONE 12:6, pages e0179286.
Crossref
S. Visser, R. Nicks, O. Faugeras & S. Coombes. (2017) Standing and travelling waves in a spherical brain model: The Nunez model revisited. Physica D: Nonlinear Phenomena 349, pages 27-45.
Crossref
Zachary P. Kilpatrick. (2016) Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction. Discrete and Continuous Dynamical Systems - Series B 21:7, pages 2211-2231.
Crossref
Yanyan Claire Ji & Flavio H. Fenton. (2016) Numerical solutions of reaction-diffusion equations: Application to neural and cardiac models. American Journal of Physics 84:8, pages 626-638.
Crossref
Christoph S. Herrmann, Micah M. Murray, Silvio Ionta, Axel Hutt & Jérémie Lefebvre. (2016) Shaping Intrinsic Neural Oscillations with Periodic Stimulation. The Journal of Neuroscience 36:19, pages 5328-5337.
Crossref
Axel Hutt & Jérémie Lefebvre. 2016. Selforganization in Complex Systems: The Past, Present, and Future of Synergetics. Selforganization in Complex Systems: The Past, Present, and Future of Synergetics 8 24 .
Romain Veltz, Pascal Chossat & Olivier Faugeras. (2015) On the Effects on Cortical Spontaneous Activity of the Symmetries of the Network of Pinwheels in Visual Area V1. The Journal of Mathematical Neuroscience 5:1.
Crossref
Eric J. Nichols & Axel Hutt. (2015) Neural field simulator: two-dimensional spatio-temporal dynamics involving finite transmission speed. Frontiers in Neuroinformatics 9.
Crossref
Meysam Hashemi, Axel Hutt & Jamie Sleigh. (2015) How the cortico-thalamic feedback affects the EEG power spectrum over frontal and occipital regions during propofol-induced sedation. Journal of Computational Neuroscience 39:2, pages 155-179.
Crossref
Zachary P. Kilpatrick. (2015) Delay stabilizes stochastic motion of bumps in layered neural fields. Physica D: Nonlinear Phenomena 295-296, pages 30-45.
Crossref
Axel Hutt, Meysam Hashemi & Peter beim Graben. 2015. Validating Neuro-Computational Models of Neurological and Psychiatric Disorders. Validating Neuro-Computational Models of Neurological and Psychiatric Disorders 141 159 .
H. Henke, P.A. Robinson, P.M. Drysdale & P.N. Loxley. (2014) Spatiotemporally varying visual hallucinations: I. Corticothalamic theory. Journal of Theoretical Biology 357, pages 200-209.
Crossref
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 349 404 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 319 345 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 271 318 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 233 269 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 185 231 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 137 181 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 101 136 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 63 99 .
Paul C. BressloffPaul C. Bressloff. 2014. Waves in Neural Media. Waves in Neural Media 3 62 .
P.A. Robinson. (2011) Neural field theory of synaptic plasticity. Journal of Theoretical Biology 285:1, pages 156-163.
Crossref
Axel Hutt & Andre Longtin. (2009) Effects of the anesthetic agent propofol on neural populations. Cognitive Neurodynamics 4:1, pages 37-59.
Crossref
J. Lefebvre, A. Longtin & V. G. Leblanc. (2010) Oscillatory response in a sensory network of ON and OFF cells with instantaneous and delayed recurrent connections. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368:1911, pages 455-467.
Crossref
Shigeru Kubota, Kosuke Hamaguchi & Kazuyuki Aihara. (2009) Local excitation solutions in one-dimensional neural fields by external input stimuli. Neural Computing and Applications 18:6, pages 591-602.
Crossref
H. Henke, P. A. Robinson, P. M. Drysdale & P. N. Loxley. (2009) Spatiotemporal dynamics of pattern formation in the primary visual cortex and hallucinations. Biological Cybernetics 101:1, pages 3-18.
Crossref
C. A. Brackley & M. S. Turner. (2009) Two-point heterogeneous connections in a continuum neural field model. Biological Cybernetics 100:5, pages 371-383.
Crossref
M. A. DAHLEM, G. HILLER, A. PANCHUK & E. SCHÖLL. (2011) DYNAMICS OF DELAY-COUPLED EXCITABLE NEURAL SYSTEMS. International Journal of Bifurcation and Chaos 19:02, pages 745-753.
Crossref
Thomas Wennekers. (2008) Tuned solutions in dynamic neural fields as building blocks for extended EEG models. Cognitive Neurodynamics 2:2, pages 137-146.
Crossref
A. Wilmer, T. D. Frank, P. J. Beek & R. Friedrich. (2007) A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems. The European Physical Journal B 60:2, pages 203-215.
Crossref
Øyvind Nordbø, John Wyller & Gaute T. Einevoll. (2007) Neural network firing-rate models on integral form. Biological Cybernetics 97:3, pages 195-209.
Crossref
M. T. Wilson, Moira L. Steyn-Ross, D. A. Steyn-Ross & J. W. Sleigh. (2008) Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics. Journal of Biological Physics 33:3, pages 213-246.
Crossref
A. Hutt & T.D. Frank. (2005) Critical Fluctuations and 1/f α -Activity of Neural Fields Involving Transmission Delays . Acta Physica Polonica A 108:6, pages 1021-1040.
Crossref
M. T. Wilson, M. L. Steyn-Ross, D. A. Steyn-Ross & J. W. Sleigh. (2005) Predictions and simulations of cortical dynamics during natural sleep using a continuum approach. Physical Review E 72:5.
Crossref
S. Coombes. (2005) Waves, bumps, and patterns in neural field theories. Biological Cybernetics 93:2, pages 91-108.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.