PMID: 486593Oct 1, 1979

A mathematical theory of visual hallucination patterns

Biological cybernetics
G B Ermentrout, Jack D Cowan

Abstract

Neuronal activity in a two-dimensional net is analyzed in the neighborhood of an instability. Bifurcation theory and group theory are used to demonstrate the existence of a variety of doubly-periodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity. It is suggested that these simple geometric patterns are the cortical concomitants of the "form constants" seen during visual hallucinosis.

References

Apr 18, 1979·Journal of Mathematical Biology·G B Ermentrout, J D Cowan
Mar 1, 1978·The American Journal of Psychiatry·R K Siegel
Oct 1, 1977·Scientific American·R K Siegel
May 1, 1971·Scientific American·W Richards
Feb 1, 1963·Archives of Ophthalmology·A E KRILLA M OSTFELD
Dec 1, 1963·Brain : a Journal of Neurology·W PENFIELD, P PEROT
Feb 9, 1965·Zeitschrift für Zellforschung und mikroskopische Anatomie·K FUXE

Citations

Jan 1, 1993·Biological cybernetics·H J Chang, J Ghosh
Jan 1, 1995·Biological cybernetics·J G Taylor, F N Alavi
Jan 1, 1985·Journal of Mathematical Biology·G B Ermentrout
Jan 1, 1984·Biological cybernetics·H J Reitboeck, J Altmann
Jan 1, 1983·Bulletin of Mathematical Biology·A Muir, M W Warner
Apr 8, 2009·Biological cybernetics·C A Brackley, M S Turner
Jul 2, 2009·Journal of Computational Neuroscience·Birgit KrienerStefan Rotter
Mar 9, 2011·Journal of Computational Neuroscience·Jonathan D Touboul, G B Ermentrout
Jun 15, 2011·Journal of Computational Neuroscience·Zachary P Kilpatrick, G Bard Ermentrout
Oct 26, 2012·Journal of Computational Neuroscience·Aaditya V Rangan, Lai-Sang Young
Aug 12, 2009·Journal of Biological Physics·Axel Hutt, Lutz Schimansky-Geier
Jun 7, 2005·Current Psychiatry Reports·Dominic H Ffytche
Mar 1, 1996·Computers in Biology and Medicine·J A Reggia, D Montgomery
Feb 10, 2004·Journal of Physiology, Paris·Boris S GutkinBard Ermentrout
Feb 10, 2004·Journal of Physiology, Paris·Paul C Bressloff, Jack D Cowan
Feb 10, 2004·Journal of Physiology, Paris·Jean Petitot
Feb 10, 2004·Journal of Physiology, Paris·Yves Frégnac
Dec 24, 2003·Neural Networks : the Official Journal of the International Neural Network Society·S M StringerT P Trappenberg
Mar 1, 1997·Journal of Biological Physics·Peter A Tass
Jul 22, 2006·Nature Reviews. Neuroscience·Bruce L McNaughtonMay-Britt Moser
Mar 11, 2000·The European Journal of Neuroscience·M A DahlemS C Müller
Dec 29, 2011·Proceedings of the National Academy of Sciences of the United States of America·Thomas Charles ButlerJack D Cowan
Jan 15, 2000·Neural Computation·Paul C Bressloff, S Coombes
Aug 23, 2001·Neural Computation·J Eggert, J L van Hemmen
Feb 28, 2002·Neural Computation·Paul C BressloffM C Wiener
Feb 28, 2002·Neural Computation·Paul C Bressloff, Jack D Cowan
Oct 23, 1997·Neural Computation·D Horn, I Opher
May 25, 2007·Neural Computation·Naoki MasudaKazuyuki Aihara
Feb 10, 2009·Neural Computation·Konstantin Doubrovinski, J Michael Herrmann
Oct 27, 2009·Neural Computation·Michael A BuiceCarson C Chow
Apr 28, 2011·Neural Computation·Dequan JinBin Li
Sep 5, 2008·PLoS Computational Biology·Gustavo DecoKarl J Friston
Aug 12, 2010·PLoS Computational Biology·Sandro Romani, Misha Tsodyks
Oct 8, 2011·PLoS Computational Biology·Michael RuleBard Ermentrout
Jan 30, 2013·PLoS Computational Biology·Michael A Buice, Carson C Chow
Dec 19, 2013·PloS One·Tomoko Sakiyama, Yukio-Pegio Gunji
Jun 1, 1995·Chaos·Peter Jung, Gottfried Mayer-Kress
Feb 9, 2011·Neural Computation·Yao LuShun-Ichi Amari
May 2, 2007·Proceedings of the National Academy of Sciences of the United States of America·Vincent A Billock, Brian H Tsou
Dec 29, 2005·Proceedings of the National Academy of Sciences of the United States of America·Aaditya V RanganDavid W McLaughlin
Jan 1, 1982·Biological cybernetics·Christoph von der Malsburg, Jack D Cowan
Feb 26, 2003·Proceedings of the National Academy of Sciences of the United States of America·Kukjin KangHaim Sompolinsky
Nov 7, 2008·Journal of Mathematical Biology·Junmei Zhu, Christoph von der Malsburg
Sep 1, 1996·Neurochemical Research·N F Britton, S M Skevington
Jan 23, 2016·Nature Communications·Selen AtasoyJoel Pearson
Mar 5, 2016·Frontiers in Computational Neuroscience·Ahmed A MoustafaDorota Frydecka
Sep 5, 2012·Journal of Physiology, Paris·Xiaogang YanTai Sing Lee
Apr 11, 2015·Journal of Mathematical Neuroscience·Ehsan NegahbaniJamie W Sleigh
Jun 10, 2015·Journal of Mathematical Neuroscience·Romain VeltzOlivier Faugeras
Apr 9, 2015·Journal of Mathematical Neuroscience·Paul C Bressloff
Aug 30, 2011·Current Opinion in Neurobiology·Li Zhaoping
May 18, 2010·Epilepsy & Behavior : E&B·John G Milton
Aug 22, 2009·Progress in Biophysics and Molecular Biology·Michael A Buice, Jack D Cowan
Jun 16, 2009·Journal of Physiology, Paris·Tanya I Baker, Jack D Cowan
Sep 14, 2015·Neural Networks : the Official Journal of the International Neural Network Society·Dequan Jin, Jigen Peng
Jan 15, 2005·Progress in Neurobiology·M A Dahlem, E P Chronicle
Aug 1, 1989·Immunological Reviews·A S Perelson
Mar 11, 2006·International Journal of Psychophysiology : Official Journal of the International Organization of Psychophysiology·Hermann Haken
Apr 5, 2016·Journal of Mathematical Neuroscience·Paul C BressloffPeter J Thomas
Dec 1, 1990·Differentiation; Research in Biological Diversity·L Edelstein-Keshet, G B Ermentrout
Aug 19, 2015·Progress in Biophysics and Molecular Biology·Ralph Abraham
Feb 15, 2012·Journal of Neuroscience Methods·P A Robinson, J W Kim
Jun 2, 2012·NeuroImage·James A Roberts, P A Robinson
Dec 9, 2010·NeuroImage·D A Pinotsis, Karl J Friston
Jan 8, 2000·Developmental Biology·M R OwenH J Wearing
Feb 14, 2015·Biological cybernetics·M FotouhiM Sharifitabar
Feb 22, 2014·Clinical Neurophysiology : Official Journal of the International Federation of Clinical Neurophysiology·Anne BeuterJulien Modolo
Jan 26, 2010·NeuroImage·Stephen Coombes
Apr 29, 2009·NeuroImage·Jean DaunizeauKarl J Friston
Oct 3, 2015·Chaos·Martin Golubitsky, Ian Stewart
Jul 19, 2014·Behavioural Brain Research·Adam L Halberstadt
May 31, 2014·Journal of Theoretical Biology·H HenkeP N Loxley
Mar 6, 2015·Frontiers in Neurology·Jos J Eggermont, Peter A Tass
May 24, 2001·Journal of Theoretical Biology·C T LeeA Mogilner
Oct 23, 2015·PLoS Computational Biology·Paul C Bressloff, Samuel R Carroll
Feb 18, 2015·PLoS Computational Biology·L R González-RamírezM A Kramer
Jun 20, 2016·Current Opinion in Neurobiology·Paul Miller
Jun 25, 2016·Wiley Interdisciplinary Reviews. Systems Biology and Medicine·Constantinos Siettos, Jens Starke
Oct 12, 2016·ELife·Joel PearsonBard Ermentrout
Dec 2, 2016·Behavioral and Brain Functions : BBF·Hina AbidSafee U Chaudhary
Aug 6, 2016·PLoS Computational Biology·Diego FasoliStefano Panzeri
Jul 14, 1983·Nature·F Crick, G Mitchison
Apr 8, 2017·Psychopharmacology·Rainer KraehenmannFranz X Vollenweider
Jan 7, 1988·Journal of Theoretical Biology·J L Eilbert
Apr 20, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Patrick D Roberts
Oct 28, 2017·Journal of Mathematical Neuroscience·Aytül GökçeStephen Coombes
Sep 3, 2017·The Neuroscientist : a Review Journal Bringing Neurobiology, Neurology and Psychiatry·Selen AtasoyJoel Pearson
Jan 9, 1995·Physical Review Letters·M UsherZ Olami
Jun 12, 2018·International Journal of Neural Systems·Michael Caiola, Mark H Holmes
Apr 24, 2001·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Paul C BressloffM C Wiener
Dec 6, 2001·Nature Reviews. Molecular Cell Biology·J J TysonB Novak
Jan 6, 2016·Journal of Mathematical Neuroscience·Jack D CowanWim van Drongelen
May 19, 2005·Biological cybernetics·Máté LengyelPéter Erdi
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Grigory Bordyugov, Harald Engel
Nov 13, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Paul C Bressloff, Zachary P Kilpatrick
Aug 2, 2005·Biological cybernetics·Stephen Coombes
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Paul C Bressloff
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P A Robinson
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·James A Roberts, P A Robinson
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zachary P Kilpatrick, Bard Ermentrout
Mar 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pere ColetDamià Gomila
Oct 3, 2017·PLoS Computational Biology·Tiziano D'Albis, Richard Kempter
Nov 5, 2019·PLoS Computational Biology·Michael E RuleGuido Sanguinetti
Nov 7, 2019·Biological cybernetics·L R González-Ramírez, Ava J Mauro
Nov 28, 2019·Journal of Neurophysiology·Áine ByrneStephen Coombes
Aug 23, 2002·Physical Review Letters·Paul C Bressloff
Mar 19, 2020·Journal of Neurophysiology·Carson C Chow, Yahya Karimipanah
Sep 3, 2020·PLoS Computational Biology·Stewart Heitmann, Bard Ermentrout
Feb 11, 2020·Frontiers in Computational Neuroscience·Isma ZulfiqarElia Formisano
Mar 1, 2013·Journal of Statistical Mechanics : Theory and Experiment·Michael A Buice, Carson C Chow
Aug 31, 2016·Physical Review. E·Rehman AliBard Ermentrout
Oct 12, 2017·Journal of Mathematical Neuroscience·Andrea K BarreiroEli Shlizerman
Feb 20, 2019·Physical Review. E·Áine ByrneStephen Coombes
Aug 1, 1988·Quarterly Reviews of Biophysics·J D Cowan, D H Sharp
May 10, 2017·Frontiers in Computational Neuroscience·Yanqing Chen
Aug 5, 2017·Physical Review Letters·Mauro M Monsalve-Mercado, Christian Leibold
Feb 1, 2020·Journal of Mathematical Neuroscience·Pascal Chossat
Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J Eggert, J L van Hemmen
Aug 17, 2019·Frontiers in Computational Neuroscience·Daniel Naoumenko, Pulin Gong
May 26, 2018·Journal of Computational Neuroscience·L R González-Ramírez, M A Kramer
Mar 7, 2019·Nature Communications·James A RobertsMichael Breakspear
Nov 30, 2019·Frontiers in Psychology·Khalil Iskarous
Oct 22, 2020·Scientific Reports·Rubén HerzogRodrigo Cofre
Jan 5, 2021·Journal of Mathematical Neuroscience·Ugo BoscainGiuseppina Turco

Related Concepts

Nerve Impulses
Hallucinations, Visual, Unformed
Resting Potentials
Neural Networks (Anatomic)
Neural Inhibition
Periodicity
Vision
Visual Cortex
Visual Fields

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