Dynamics of pattern formation in lateral-inhibition type neural fields

The chemical basis of morphogenesis

Turing, A. M. (1952) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1952.0012 · Cited by 11,733

Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons

Wilson, H. R., & Cowan, J. D. (1972) · Biophysical Journal · doi:10.1016/s0006-3495(72)86068-5 · Cited by 3,623

A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

Wilson, H. R., & Cowan, J. D. (1973) · Kybernetik · doi:10.1007/bf00288786 · Cited by 1,850

The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle.

Wiener, N., & Rosenblueth, A. (1946) · PubMed · Cited by 520

Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements

Amari, S.-I. (1972) · IEEE Transactions on Computers · doi:10.1109/t-c.1972.223477 · Cited by 474

Some mathematical questions in biology

Levin, S. A., & Cowan, J. D. (1970) · American Mathematical Society eBooks · Cited by 435

Properties of a mass of cells capable of regenerating pulses

Beurle, R. L. (1956) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1956.0012 · Cited by 380

Competition and Cooperation in Neural Nets

AMARI, S.-I., & ARBIB, M. A. (1977) · Systems Neuroscience · doi:10.1016/b978-0-12-491850-4.50009-x · Cited by 378

Characteristics of Random Nets of Analog Neuron-Like Elements

Amarimber, S.-I. (1972) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1972.4309193 · Cited by 300

Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks

Ellias, S. A., & Grossberg, S. (1975) · Biological Cybernetics · doi:10.1007/bf00327046 · Cited by 271

Path integration and the neural basis of the 'cognitive map'

McNaughton, B. L., Battaglia, F. P., Jensen, O., Moser, E. I., & Moser, M.-B. (2006) · Nature Reviews Neuroscience · doi:10.1038/nrn1932 · Cited by 2,024

Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit

Hahnloser, R. H. R., Sarpeshkar, R., Mahowald, M. A., Douglas, R. J., & Seung, H. S. (2000) · Nature · doi:10.1038/35016072 · Cited by 1,293

Dynamic models of large-scale brain activity

Breakspear, M. (2017) · Nature Neuroscience · doi:10.1038/nn.4497 · Cited by 1,239

Synaptic Mechanisms and Network Dynamics Underlying Spatial Working Memory in a Cortical Network Model

Compte, A. (2000) · Cerebral Cortex · doi:10.1093/cercor/10.9.910 · Cited by 1,143

Synaptic reverberation underlying mnemonic persistent activity

Wang, X.-J. (2001) · Trends in Neurosciences · doi:10.1016/s0166-2236(00)01868-3 · Cited by 1,059

The dynamic brain: from spiking neurons to neural masses and cortical fields

Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M., & Friston, K. (2008) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000092 · Cited by 1,084

Path integration and cognitive mapping in a continuous attractor neural network model

Samsonovich, A., & McNaughton, B. L. (1997) · The Journal of Neuroscience · doi:10.1523/jneurosci.17-15-05900.1997 · Cited by 989

Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory

Wang, X.-J. (1999) · The Journal of Neuroscience · doi:10.1523/jneurosci.19-21-09587.1999 · Cited by 859

A model of saccade generation based on parallel processing and competitive inhibition

Findlay, J. M., & Walker, R. (1999) · Behavioral and Brain Sciences · doi:10.1017/s0140525x99002150 · Cited by 730

Dynamic Systems Theories

Thelen, E., & Smith, L. B. (2007) · Handbook of Child Psychology · doi:10.1002/9780470147658.chpsy0106 · Cited by 729

Spatial representation in the hippocampal formation: a history

Moser, E. I., Moser, M.-B., & McNaughton, B. L. (2017) · Nature Neuroscience · doi:10.1038/nn.4653 · Cited by 560

A computational theory of hippocampal function, and empirical tests of the theory

Rolls, E. T., & Kesner, R. P. (2006) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2006.04.005 · Cited by 608

Computational Neuroscience of Vision

Rolls, E., & Deco, G. (2001) · doi:10.1093/acprof:oso/9780198524885.001.0001 · Cited by 553

The mechanisms for pattern completion and pattern separation in the hippocampus

Rolls, E. T. (2013) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2013.00074 · Cited by 545

A model of saccade initiation based on the competitive integration of exogenous and endogenous signals in the superior colliculus

Trappenberg, T. P., Dorris, M. C., Munoz, D. P., & Klein, R. M. (2001) · Journal of Cognitive Neuroscience · doi:10.1162/089892901564306 · Cited by 443

Waves, bumps, and patterns in neural field theories

Coombes, S. (2005) · Biological Cybernetics · doi:10.1007/s00422-005-0574-y · Cited by 447

Human Reasoning and Cognitive Science

Stenning, K., & van Lambalgen, M. (2008) · The MIT Press eBooks · doi:10.7551/mitpress/7964.001.0001 · Cited by 437

Toroidal topology of population activity in grid cells

Gardner, R. J., Hermansen, E., Pachitariu, M., Burak, Y., Baas, N. A., Dunn, B. A., Moser, M.-B., & Moser, E. I. (2022) · Nature · doi:10.1038/s41586-021-04268-7 · Cited by 428

Recurrent inhibitory circuitry as a mechanism for grid formation

Couey, J. J., Witoelar, A., Zhang, S.-J., Zheng, K., Ye, J., Dunn, B., Czajkowski, R., Moser, M.-B., Moser, E. I., Roudi, Y., et al. (2013) · Nature Neuroscience · doi:10.1038/nn.3310 · Cited by 422

Ring attractor dynamics in the Drosophila central brain

Kim, S. S., Rouault, H., Druckmann, S., & Jayaraman, V. (2017) · Science · doi:10.1126/science.aal4835 · Cited by 417

Spatiotemporal dynamics of continuum neural fields

Bressloff, P. C. (2012) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/45/3/033001 · Cited by 414

Statistical neurodynamics of associative memory

Amari, S.-I., & Maginu, K. (1988) · Neural Networks · doi:10.1016/0893-6080(88)90022-6 · Cited by 411

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

Daunizeau, J., Adam, V., & Rigoux, L. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003441 · Cited by 385

The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep

Chaudhuri, R., Gerçek, B., Pandey, B., Peyrache, A., & Fiete, I. (2019) · Nature Neuroscience · doi:10.1038/s41593-019-0460-x · Cited by 373

Mathematical framework for large-scale brain network modeling in The Virtual Brain

Sanz-Leon, P., Knock, S. A., Spiegler, A., & Jirsa, V. K. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.01.002 · Cited by 356

A computational theory of hippocampal function, and tests of the theory: New developments

Kesner, R. P., & Rolls, E. T. (2015) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2014.11.009 · Cited by 347

Dynamic causal modelling: A critical review of the biophysical and statistical foundations

Daunizeau, J., David, O., & Stephan, K. E. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2009.11.062 · Cited by 331

Grid cells and cortical representation

Moser, E. I., Roudi, Y., Witter, M. P., Kentros, C., Bonhoeffer, T., & Moser, M.-B. (2014) · Nature Reviews Neuroscience · doi:10.1038/nrn3766 · Cited by 335

Dynamics of behavior: Theory and applications for autonomous robot architectures

Schöner, G., Dose, M., & Engels, C. (1995) · Robotics and Autonomous Systems · doi:10.1016/0921-8890(95)00049-6 · Cited by 334

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

Abdelnour, F., Voss, H. U., & Raj, A. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2013.12.039 · Cited by 270

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

Ritter, P., Schirner, M., McIntosh, A. R., & Jirsa, V. K. (2013) · Brain Connectivity · doi:10.1089/brain.2012.0120 · Cited by 268

Pattern separation, completion, and categorisation in the hippocampus and neocortex

Rolls, E. T. (2016) · Neurobiology of Learning and Memory · doi:10.1016/j.nlm.2015.07.008 · Cited by 234

The Neuroanatomical Ultrastructure and Function of a Biological Ring Attractor

Turner-Evans, D. B., Jensen, K. T., Ali, S., Paterson, T., Sheridan, A., Ray, R. P., Wolff, T., Lauritzen, J. S., Rubin, G. M., Bock, D. D., et al. (2020) · Neuron · doi:10.1016/j.neuron.2020.08.006 · Cited by 168

Changes in Community Structure of Resting State Functional Connectivity in Unipolar Depression

Lord, A., Horn, D., Breakspear, M., & Walter, M. (2012) · PLoS ONE · doi:10.1371/journal.pone.0041282 · Cited by 174

The neuroanatomical ultrastructure and function of a biological ring attractor

Turner-Evans, D. B., Jensen, K. T., Ali, S., Paterson, T., Sheridan, A., Ray, R. P., Wolff, T., Lauritzen, S., Rubin, G. M., Bock, D., et al. (2019) · doi:10.1101/847152 · Cited by 166

Systematic Fluctuation Expansion for Neural Network Activity Equations

Buice, M. A., Cowan, J. D., & Chow, C. C. (2010) · Neural Computation · doi:10.1162/neco.2009.02-09-960 · Cited by 164

The dynamical stability of reverberatory neural circuits

Tegnér, J., Compte, A., & Wang, X.-J. (2002) · Biological Cybernetics · doi:10.1007/s00422-002-0363-9 · Cited by 150

Mechanisms Underlying the Neural Computation of Head Direction

Hulse, B. K., & Jayaraman, V. (2020) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-072116-031516 · Cited by 130

Robot Learning From Randomized Simulations: A Review

Muratore, F., Ramos, F., Turk, G., Yu, W., Gienger, M., & Peters, J. (2022) · Frontiers in Robotics and AI · doi:10.3389/frobt.2022.799893 · Cited by 128

Dynamics and Computation of Continuous Attractors

Wu, S., Hamaguchi, K., & Amari, S.-I. (2008) · Neural Computation · doi:10.1162/neco.2008.10-06-378 · Cited by 121

The geometry of decision-making in individuals and collectives

Sridhar, V. H., Li, L., Gorbonos, D., Nagy, M., Schell, B. R., Sorochkin, T., Gov, N. S., & Couzin, I. D. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2102157118 · Cited by 120

Grid cell co-activity patterns during sleep reflect spatial overlap of grid fields during active behaviors

Trettel, S. G., Trimper, J. B., Hwaun, E., Fiete, I. R., & Colgin, L. L. (2019) · Nature Neuroscience · doi:10.1038/s41593-019-0359-6 · Cited by 108

Closed-loop cortical neuromodulation in Parkinson’s disease: An alternative to deep brain stimulation?

Beuter, A., Lefaucheur, J.-P., & Modolo, J. (2014) · Clinical Neurophysiology · doi:10.1016/j.clinph.2014.01.006 · Cited by 107

The head direction circuit of two insect species

Pisokas, I., Heinze, S., & Webb, B. (2020) · eLife · doi:10.7554/elife.53985 · Cited by 84

Learning-induced dynamic receptive field changes in primary auditory cortex of the unanaesthetized Mongolian gerbil

Ohl, F. W., & Scheich, H. (1997) · Journal of Comparative Physiology A: Sensory, Neural, and Behavioral Physiology · doi:10.1007/s003590050150 · Cited by 85

Network mechanisms underlying the role of oscillations in cognitive tasks

Schmidt, H., Avitabile, D., Montbrió, E., & Roxin, A. (2018) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1006430 · Cited by 72

Dynamic and reversible remapping of network representations in an unchanging environment

Low, I. I. C., Williams, A. H., Campbell, M. G., Linderman, S. W., & Giocomo, L. M. (2021) · Neuron · doi:10.1016/j.neuron.2021.07.005 · Cited by 70

Synaptic Scaling Enables Dynamically Distinct Short- and Long-Term Memory Formation

Tetzlaff, C., Kolodziejski, C., Timme, M., Tsodyks, M., & Wörgötter, F. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003307 · Cited by 54

Continuous attractors with morphed/correlated maps

Romani, S., & Tsodyks, M. (2010) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000869 · Cited by 39

Beyond dimension reduction: stable electric fields emerge from and allow representational drift

Pinotsis, D. A., & Miller, E. K. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119058 · Cited by 37

Are Automatic Imitation and Spatial Compatibility Mediated by Different Processes?

Cooper, R. P., Catmur, C., & Heyes, C. (2013) · Cognitive Science · doi:10.1111/j.1551-6709.2012.01252.x · Cited by 37

Bayesian inference in ring attractor networks

Kutschireiter, A., Basnak, M. A., Wilson, R. I., & Drugowitsch, J. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2210622120 · Cited by 36

Parallel and distributed neural models of the ideomotor principle: An investigation of imitative cortical pathways

Sauser, E. L., & Billard, A. G. (2006) · Neural Networks · doi:10.1016/j.neunet.2006.02.003 · Cited by 33

Emergence of functional and structural properties of the head direction system by optimization of recurrent neural networks

Cueva, C. J., Wang, P. Y., Chin, M., & Wei, X.-X. (2019) · arXiv · doi:10.48550/arxiv.1912.10189 · Cited by 27

Encoding certainty in bump attractors

Carroll, S., Josić, K., & Kilpatrick, Z. P. (2014) · Journal of Computational Neuroscience · doi:10.1007/s10827-013-0486-0 · Cited by 23

A theoretical account of cue averaging in the rodent head direction system

Page, H. J. I., Walters, D. M., Knight, R., Piette, C. E., Jeffery, K. J., & Stringer, S. M. (2014) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2013.0283 · Cited by 21

A neural field model for color perception unifying assimilation and contrast

Song, A., Faugeras, O., & Veltz, R. (2019) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1007050 · Cited by 18

Lattice physics approaches for neural networks

Bardella, G., Franchini, S., Pani, P., & Ferraina, S. (2024) · iScience · doi:10.1016/j.isci.2024.111390 · Cited by 17

Correcting pose estimates during tactile exploration of object shape: a neuro-robotic study

Strub, C., Worgotter, F., Ritter, H., & Sandamirskaya, Y. (2014) · 4th International Conference on Development and Learning and on Epigenetic Robotics · doi:10.1109/devlrn.2014.6982950 · Cited by 15