Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration

[1]  G. Ermentrout,et al.  Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation , 2014 .

[2]  David J. B. Lloyd,et al.  Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disc , 2013 .

[3]  Zachary P. Kilpatrick Short term synaptic depression improves information transfer in perceptual multistability , 2013, Front. Comput. Neurosci..

[4]  Pierre Kornprobst,et al.  Perceptual transition dynamics of a multi-stable visual motion stimulus I: experiments , 2012 .

[5]  Olivier D. Faugeras,et al.  Bifurcation analysis applied to a model of motion integration with a multistable stimulus , 2012, Journal of Computational Neuroscience.

[6]  Alexander Pastukhov,et al.  The Role of Attention in Ambiguous Reversals of Structure-From-Motion , 2012, PloS one.

[7]  Daniel Pressnitzer,et al.  The initial phase of auditory and visual scene analysis , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[8]  Pierre Kornprobst,et al.  Motion direction integration following the onset of multistable stimuli (I): dynamic shifts in both perception and eye movements depend on signal strength , 2012 .

[9]  M. Carandini,et al.  Normalization as a canonical neural computation , 2011, Nature Reviews Neuroscience.

[10]  Paul C. Bressloff,et al.  Neural field model of binocular rivalry waves , 2012, Journal of Computational Neuroscience.

[11]  Zachary P. Kilpatrick,et al.  Hallucinogen persisting perception disorder in neuronal networks with adaptation , 2012, Journal of Computational Neuroscience.

[12]  P. Bressloff Spatiotemporal dynamics of continuum neural fields , 2012 .

[13]  R. Veltz Nonlinear analysis methods in neural field models , 2011 .

[14]  Gustavo Deco,et al.  Human Neuroscience Original Research Article Cortical Microcircuit Dynamics Mediating Binocular Rivalry: the Role of Adaptation in Inhibition , 2022 .

[15]  Stefanos E. Folias,et al.  Nonlinear Analysis of Breathing Pulses in a Synaptically Coupled Neural Network , 2011, SIAM J. Appl. Dyn. Syst..

[16]  Pascal Chossat,et al.  Analysis of a hyperbolic geometric model for visual texture perception , 2011, Journal of mathematical neuroscience.

[17]  G. Deco,et al.  Neuronal Adaptation Effects in Decision Making , 2011, The Journal of Neuroscience.

[18]  Pierre Kornprobst,et al.  A Neural Field Model for Motion Estimation , 2011 .

[19]  M. Haragus,et al.  Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems , 2010 .

[20]  Paul C. Bressloff,et al.  Binocular Rivalry in a Competitive Neural Network with Synaptic Depression , 2010, SIAM J. Appl. Dyn. Syst..

[21]  Gustavo Deco,et al.  The role of multi-area interactions for the computation of apparent motion , 2010, NeuroImage.

[22]  Peter Ashwin,et al.  A low-dimensional model of binocular rivalry using winnerless competition , 2010 .

[23]  Guillaume S Masson,et al.  Temporal dynamics of 2D motion integration for ocular following in macaque monkeys. , 2010, Journal of neurophysiology.

[24]  Olivier D. Faugeras,et al.  Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations , 2009, SIAM J. Appl. Dyn. Syst..

[25]  Rainer Klages,et al.  Applied Dynamical Systems , 2010 .

[26]  David Terman,et al.  Mathematical foundations of neuroscience , 2010 .

[27]  C. Clifford Binocular rivalry , 2009, Current Biology.

[28]  Roman Borisyuk,et al.  Visual perception of ambiguous figures: synchronization based neural models , 2009, Biological Cybernetics.

[29]  Stephen G Lisberger,et al.  Relationship between adapted neural population responses in MT and motion adaptation in speed and direction of smooth-pursuit eye movements. , 2009, Journal of neurophysiology.

[30]  Nava Rubin,et al.  Balance between noise and adaptation in competition models of perceptual bistability , 2009, Journal of Computational Neuroscience.

[31]  Paul C Bressloff,et al.  Nonlocal Ginzburg-Landau equation for cortical pattern formation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Nava Rubin,et al.  Mechanisms for Frequency Control in Neuronal Competition Models , 2008, SIAM J. Appl. Dyn. Syst..

[33]  Guillaume S. Masson,et al.  Dynamics of distributed 1D and 2D motion representations for short-latency ocular following , 2008, Vision Research.

[34]  Geoffrey M Boynton,et al.  The Representation of Behavioral Choice for Motion in Human Visual Cortex , 2007, The Journal of Neuroscience.

[35]  S. Coombes,et al.  Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities , 2007 .

[36]  J. Rinzel,et al.  Noise-induced alternations in an attractor network model of perceptual bistability. , 2007, Journal of neurophysiology.

[37]  Nava Rubin,et al.  Dynamical characteristics common to neuronal competition models. , 2007, Journal of neurophysiology.

[38]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[39]  Bernd Krauskopf,et al.  Numerical Continuation Methods for Dynamical Systems , 2007 .

[40]  Y. Shelepin European Conference on Visual Perception , 2006 .

[41]  Yee-Joon Kim,et al.  Stochastic resonance in binocular rivalry , 2006, Vision Research.

[42]  Alan W Freeman,et al.  Multistage model for binocular rivalry. , 2005, Journal of neurophysiology.

[43]  Stephen Coombes,et al.  Waves, bumps, and patterns in neural field theories , 2005, Biological Cybernetics.

[44]  D. Bradley,et al.  Structure and function of visual area MT. , 2005, Annual review of neuroscience.

[45]  S. Coombes,et al.  Bumps, breathers, and waves in a neural network with spike frequency adaptation. , 2005, Physical review letters.

[46]  Maria V. Sanchez-Vives,et al.  Slow adaptation in fast-spiking neurons of visual cortex. , 2005, Journal of neurophysiology.

[47]  Carson C. Chow,et al.  Existence and Stability of Standing Pulses in Neural Networks: I. Existence , 2005, SIAM J. Appl. Dyn. Syst..

[48]  Carlo R. Laing,et al.  Spiral Waves in Nonlocal Equations , 2005, SIAM J. Appl. Dyn. Syst..

[49]  Kung Yao,et al.  Perceptual dominance time distributions in multistable visual perception , 2004, Biological Cybernetics.

[50]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[51]  Bard Ermentrout,et al.  Pattern Formation in a Network of Excitatory and Inhibitory Cells with Adaptation , 2004, SIAM J. Appl. Dyn. Syst..

[52]  Carson C. Chow,et al.  A Spiking Neuron Model for Binocular Rivalry , 2004, Journal of Computational Neuroscience.

[53]  Paul C. Bressloff,et al.  Breathing Pulses in an Excitatory Neural Network , 2004, SIAM J. Appl. Dyn. Syst..

[54]  Yixin Guo,et al.  Existence and stability of standing pulses in neural networks , 2003 .

[55]  Ricardo Gattass,et al.  Electrophysiological Imaging of Functional Architecture in the Cortical Middle Temporal Visual Area of Cebus apella Monkey , 2003, The Journal of Neuroscience.

[56]  G. Lord,et al.  Waves and bumps in neuronal networks with axo-dendritic synaptic interactions , 2003 .

[57]  Nava Rubin,et al.  The dynamics of bi-stable alternation in ambiguous motion displays: a fresh look at plaids , 2003, Vision Research.

[58]  Martin Golubitsky,et al.  Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling , 2003, SIAM J. Appl. Dyn. Syst..

[59]  Carlo R. Laing,et al.  PDE Methods for Nonlocal Models , 2003, SIAM J. Appl. Dyn. Syst..

[60]  N. Rubin,et al.  Dynamics of perceptual bi-stability : plaids and binocular rivalry compared , 2003 .

[61]  Boris S. Gutkin,et al.  Multiple Bumps in a Neuronal Model of Working Memory , 2002, SIAM J. Appl. Math..

[62]  J. Zanker,et al.  The Directional Tuning of the Barber-Pole Illusion , 2001, Perception.

[63]  B. Kendall Nonlinear Dynamics and Chaos , 2001 .

[64]  R. Blake © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 5 A Primer on Binocular Rivalry, Including Current Controversies , 2000 .

[65]  M. Golubitsky,et al.  Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[66]  Bard Ermentrout,et al.  Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses , 2001, SIAM J. Appl. Math..

[67]  E. Castet,et al.  Temporal dynamics of motion integration for the initiation of tracking eye movements at ultra-short latencies , 2000, Visual Neuroscience.

[68]  Maria V. Sanchez-Vives,et al.  Cellular Mechanisms of Long-Lasting Adaptation in Visual Cortical Neurons In Vitro , 2000, The Journal of Neuroscience.

[69]  P. Chossat,et al.  Methods in Equivariant Bifurcations and Dynamical Systems , 2000 .

[70]  G. Orban,et al.  Response latency of macaque area MT/V5 neurons and its relationship to stimulus parameters. , 1999, Journal of neurophysiology.

[71]  Eric Castet,et al.  The extrinsic/intrinsic classification of two-dimensional motion signals with barber-pole stimuli , 1999, Vision Research.

[72]  M. Giese Dynamic neural field theory for motion perception , 1998 .

[73]  Frans A. J. Verstraten,et al.  The Motion Aftereffect:A Modern Perspective , 1998 .

[74]  Y. Kuznetsov Elements of applied bifurcation theory (2nd ed.) , 1998 .

[75]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .

[76]  B. Ermentrout Neural networks as spatio-temporal pattern-forming systems , 1998 .

[77]  H. Wallach On the visually perceived direction of motion ' ' by Hans Wallach : 60 years later , 1997 .

[78]  Thomas F. Fairgrieve,et al.  AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) , 1997 .

[79]  David A. Leopold,et al.  What is rivalling during binocular rivalry? , 1996, Nature.

[80]  N. Logothetis,et al.  Activity changes in early visual cortex reflect monkeys' percepts during binocular rivalry , 1996, Nature.

[81]  S. Nelson,et al.  An emergent model of orientation selectivity in cat visual cortical simple cells , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[82]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[83]  T. Papathomas Early vision and beyond , 1995 .

[84]  S. R. Lehky Binocular rivalry is not chaotic , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[85]  Y. Kuznetsov Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[86]  S. Yamane,et al.  Neural activity in cortical area MST of alert monkey during ocular following responses. , 1994, Journal of neurophysiology.

[87]  M. Shiffrar,et al.  Different motion sensitive units are involved in recovering the direction of moving lines , 1993, Vision Research.

[88]  Maggie Shiffrar,et al.  The influence of terminators on motion integration across space , 1992, Vision Research.

[89]  John H. R. Maunsell,et al.  Coding of image contrast in central visual pathways of the macaque monkey , 1990, Vision Research.

[90]  N. Logothetis,et al.  Neuronal correlates of subjective visual perception. , 1989, Science.

[91]  R. Blake A neural theory of binocular rivalry. , 1989, Psychological review.

[92]  G. Dangelmayr,et al.  The Takens-Bogdanov bifurcation with O(2)-symmetry , 1987, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[93]  T. Albright Direction and orientation selectivity of neurons in visual area MT of the macaque. , 1984, Journal of neurophysiology.

[94]  V. S. Ramachandran,et al.  Perceptual organization in moving patterns , 1983, Nature.

[95]  Ellen C. Hildreth,et al.  The detection of intensity changes by computer and biological vision systems , 1983, Comput. Vis. Graph. Image Process..

[96]  J. Cowan,et al.  Large Scale Spatially Organized Activity in Neural Nets , 1980 .

[97]  J. Craggs Applied Mathematical Sciences , 1973 .

[98]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[99]  Shun-ichi Amari,et al.  Characteristics of randomly connected threshold-element networks and network systems , 1971 .

[100]  H. Wallach,et al.  The kinetic depth effect. , 1953, Journal of experimental psychology.

[101]  Hans Wallach Über visuell wahrgenommene Bewegungsrichtung , 1935 .

[102]  Edgar Rubin Visuell wahrgenommene Figuren : Studien in psychologischer Analyse , 1921 .

[103]  L. A. N. Esq.,et al.  LXI. Observations on some remarkable optical phænomena seen in Switzerland; and on an optical phænomenon which occurs on viewing a figure of a crystal or geometrical solid , 1832 .

[104]  H. Sompolinsky,et al.  13 Modeling Feature Selectivity in Local Cortical Circuits , 2022 .