The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons
Open accessAbstract
Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Hebb, D. O. (2005) · doi:10.4324/9781410612403 · Cited by 9,825
Cited by
Mechanisms of Gamma Oscillations
Buzsáki, G., & Wang, X.-J. (2012) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-062111-150444 · Cited by 2,796
The time course of perceptual choice: The leaky, competing accumulator model.
Usher, M., & McClelland, J. L. (2001) · Psychological Review · doi:10.1037/0033-295x.108.3.550 · Cited by 2,152
Neurophysiological and Computational Principles of Cortical Rhythms in Cognition
Wang, X.-J. (2010) · Physiological Reviews · doi:10.1152/physrev.00035.2008 · Cited by 1,939
Emerging concepts for the dynamical organization of resting-state activity in the brain
Deco, G., Jirsa, V. K., & McIntosh, A. R. (2011) · Nature reviews. Neuroscience · doi:10.1038/nrn2961 · Cited by 1,798
Dynamic models of large-scale brain activity
Breakspear, M. (2017) · Nature Neuroscience · doi:10.1038/nn.4497 · Cited by 1,239
Compte, A. (2000) · Cerebral Cortex · doi:10.1093/cercor/10.9.910 · Cited by 1,143
A Recurrent Network Mechanism of Time Integration in Perceptual Decisions
Wong, K.-F., & Wang, X.-J. (2006) · The Journal of Neuroscience · doi:10.1523/jneurosci.3733-05.2006 · Cited by 1,029
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
An emergent model of orientation selectivity in cat visual cortical simple cells
Somers, D., Nelson, S., & Sur, M. (1995) · The Journal of Neuroscience · doi:10.1523/jneurosci.15-08-05448.1995 · Cited by 860
Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition
Gerstner, W., Kistler, W. M., Naud, R., & Paninski, L. (2014) · doi:10.1017/cbo9781107447615 · Cited by 1,515
Sleep as a fundamental property of neuronal assemblies
Krueger, J. M., Rector, D. M., Roy, S., Van Dongen, H. P. A., Belenky, G., & Panksepp, J. (2008) · Nature Reviews Neuroscience · doi:10.1038/nrn2521 · Cited by 596
Storing covariance with nonlinearly interacting neurons
Sejnowski, T. J. (1977) · Journal of Mathematical Biology · doi:10.1007/bf00275079 · Cited by 546
Vogels, T. P., Rajan, K., & Abbott, L. F. (2005) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.28.061604.135637 · Cited by 497
A unified framework for addiction: Vulnerabilities in the decision process
Redish, A. D., Jensen, S., & Johnson, A. (2008) · Behavioral and Brain Sciences · doi:10.1017/s0140525x0800472x · Cited by 501
Discrete attractor dynamics underlies persistent activity in the frontal cortex
Inagaki, H. K., Fontolan, L., Romani, S., & Svoboda, K. (2019) · Nature · doi:10.1038/s41586-019-0919-7 · Cited by 334
Exploring the network dynamics underlying brain activity during rest
Cabral, J., Kringelbach, M. L., & Deco, G. (2014) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2013.12.005 · Cited by 351
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
Eigenvalue Spectra of Random Matrices for Neural Networks
Rajan, K., & Abbott, L. F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.188104 · Cited by 320
Neural mechanisms of movement planning: motor cortex and beyond
Svoboda, K., & Li, N. (2018) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2017.10.023 · Cited by 347
A coupled attractor model of the rodent head direction system
Redish, A. D., Elga, A. N., & Touretzky, D. S. (1996) · Network: Computation in Neural Systems · doi:10.1088/0954-898x_7_4_004 · Cited by 344
Stability of the memory of eye position in a recurrent network of conductance-based model neurons
Seung, H. S., Lee, D. D., Reis, B. Y., & Tank, D. W. (2000) · Neuron · doi:10.1016/s0896-6273(00)81155-1 · Cited by 339
Are central pattern generators understandable?
Selverston, A. I. (1980) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00006580 · Cited by 319
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
Roberts, J. A., Gollo, L. L., Abeysuriya, R. G., Roberts, G., Mitchell, P. B., Woolrich, M. W., & Breakspear, M. (2019) · Nature Communications · doi:10.1038/s41467-019-08999-0 · Cited by 264
Neural masses and fields in dynamic causal modeling
Moran, R., Pinotsis, D. A., & Friston, K. (2013) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2013.00057 · Cited by 255
Neural circuits as computational dynamical systems
Sussillo, D. (2014) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2014.01.008 · Cited by 247
Optimally controlling the human connectome: the role of network topology
Betzel, R. F., Gu, S., Medaglia, J. D., Pasqualetti, F., & Bassett, D. S. (2016) · Scientific Reports · doi:10.1038/srep30770 · Cited by 247
Noradrenergic Suppression of Synaptic Transmission May Influence Cortical Signal-to-Noise Ratio
Hasselmo, M. E., Linster, C., Patil, M., Ma, D., & Cekic, M. (1997) · Journal of Neurophysiology · doi:10.1152/jn.1997.77.6.3326 · Cited by 229
Mejias, J. F., Murray, J. D., Kennedy, H., & Wang, X.-J. (2016) · Science Advances · doi:10.1126/sciadv.1601335 · Cited by 227
Computational principles of memory
Chaudhuri, R., & Fiete, I. (2016) · Nature Neuroscience · doi:10.1038/nn.4237 · Cited by 213
Physiological properties of inhibitory interneurons in cat striate cortex
Azouz, R. (1997) · Cerebral Cortex · doi:10.1093/cercor/7.6.534 · Cited by 173
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
Self-citationAssaneo, M. F., & Poeppel, D. (2018) · Science Advances · doi:10.1126/sciadv.aao3842 · Cited by 164
Usher, M., & Niebur, E. (1996) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1996.8.4.311 · Cited by 147
Cortical damping: analysis of thalamocortical response transformations in rodent barrel cortex
Pinto, D. J. (2003) · Cerebral Cortex · doi:10.1093/cercor/13.1.33 · Cited by 137
Moon, J.-Y., Lee, U., Blain-Moraes, S., & Mashour, G. A. (2015) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1004225 · Cited by 136
Topology and dynamics of the canonical circuit of cat V1
Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2009) · Neural Networks · doi:10.1016/j.neunet.2009.07.011 · Cited by 108
A perspective on cortical layering and layer-spanning neuronal elements
Larkum, M. E., Petro, L. S., Sachdev, R. N. S., & Muckli, L. (2018) · Frontiers in Neuroanatomy · doi:10.3389/fnana.2018.00056 · Cited by 102
Shomrat, T., Graindorge, N., Bellanger, C., Fiorito, G., Loewenstein, Y., & Hochner, B. (2011) · Current Biology · doi:10.1016/j.cub.2011.09.011 · Cited by 83
Wang, J. X., Cohen, N. J., & Voss, J. L. (2015) · Neurobiology of Learning and Memory · doi:10.1016/j.nlm.2014.04.003 · Cited by 75
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
Perspectives on defining cell types in the brain
Mukamel, E. A., & Ngai, J. (2019) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2018.11.007 · Cited by 56
“Perhaps the simplest paradigmatic example from computational neuroscience is the interaction between excitatory and inhibitory neural populations, as in the classic Wilson–Cowan model [82].”
MethodAitchison, L., & Lengyel, M. (2016) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005186 · Cited by 67
Metastable dynamics of neural circuits and networks
Brinkman, B. A. W., Yan, H., Maffei, A., Park, I. M., Fontanini, A., Wang, J., & La Camera, G. (2022) · Applied Physics Reviews · doi:10.1063/5.0062603 · Cited by 64
Life and Understanding: The Origins of “Understanding” in Self-Organizing Nervous Systems
Yufik, Y. M., & Friston, K. (2016) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2016.00098 · Cited by 53
Schiff, M. L., & Reyes, A. D. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00208.2011 · Cited by 48
Brain rhythms reveal a hierarchical network organization.
Steinke, G. K., & Galán, R. F. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002207 · Cited by 42
May, P. J. C., Westö, J., & Tiitinen, H. (2015) · European Journal of Neuroscience · doi:10.1111/ejn.12820 · Cited by 36
Reinforcement learning of linking and tracing contours in recurrent neural networks
Brosch, T., Neumann, H., & Roelfsema, P. R. (2015) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1004489 · Cited by 33
Discussion: McCulloch-Pitts and related neural nets from 1943 to 1989
Cowan, J. D. (1990) · Bulletin of Mathematical Biology · doi:10.1007/bf02459569 · Cited by 22
Self-citationCattani, A., Galluzzi, A., Fecchio, M., Pigorini, A., Mattia, M., & Massimini, M. (2023) · eneuro · doi:10.1523/eneuro.0435-22.2023 · Cited by 21
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
On the minimal theory of consciousness implicit in active inference
Whyte, C. J., Corcoran, A. W., Robinson, J., Smith, R., Moran, R. J., Parr, T., Friston, K. J., Seth, A. K., & Hohwy, J. (2026) · Physics of Life Reviews · doi:10.1016/j.plrev.2025.11.002 · Cited by 15
May, P. J. C., & Tiitinen, H. (2013) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2013.00152 · Cited by 14
Hajizadeh, A., Matysiak, A., May, P. J. C., & König, R. (2019) · Biological Cybernetics · doi:10.1007/s00422-019-00795-9 · Cited by 14
Hajizadeh, A., Matysiak, A., Brechmann, A., König, R., & May, P. J. C. (2021) · Psychophysiology · doi:10.1111/psyp.13769 · Cited by 9
Metadata
- Authors
- Wilson, H. R., & Cowan, J. D.
- Venue
- Biophysical Journal
- Publisher
- Elsevier BV
- Published
- 1972-01
- Volume
- 12
- Issue
- 1
- Pages
- 1-24
- ISSN
- 0006-3495 (ISSN-L)
- OpenAlex
- W2016354087
- Cited by
- 3,623
- References
- 1
- FWCI
- 10.40
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.