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Encyclopedia of Computational Neuroscience pp 1–5Cite as

Wilson-Cowan Model

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Definition

The Wilson-Cowan model describes the evolution of excitatory and inhibitory activity in a synaptically coupled neuronal network. As opposed to being a detailed biophysical model, the system is a coarse-grained description of the overall activity of a large-scale neuronal network, employing just two differential equations. Key parameters in the model are the strength of connectivity between each subtype of population (excitatory and inhibitory) and the strength of input to each subpopulation. Varying these generates a diversity of dynamical behaviors that are representative of observed activity in the brain, like multistability, oscillations, traveling waves, and spatial patterns.

Detailed Description

Many regions of the brain process large-scale spatiotemporally structured inputs (Wang 2010). Understanding the resulting neural activity requires macroscopic models that can track the average firing rate across many areas of a neuronal network (Ermentrout 1998). This was the...

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References

  • Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27(2):77–87

    Article  CAS  PubMed  Google Scholar 

  • Ben-Yishai R, Bar-Or RL, Sompolinsky H (1995) Theory of orientation tuning in visual cortex. Proc Natl Acad Sci USA 92(9):3844–3848

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Bogacz R, Brown E, Moehlis J, Holmes P, Cohen JD (2006) The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychol Rev 113(4):700–765. doi:10.1037/0033-295X.113.4.700

    Article  PubMed  Google Scholar 

  • Bressloff PC (2012) Spatiotemporal dynamics of continuum neural fields. J Phys A Math Theor 45(3):033001

    Article  Google Scholar 

  • Bressloff PC, Cowan JD (2003) A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn. Philos Trans R Soc Lond B Biol Sci 358(1438):1643–1667. doi10.1098/rstb.2002.1109

    Article  PubMed Central  PubMed  Google Scholar 

  • Bressloff PC, Cowan JD, Golubitsky M, Thomas PJ, Wiener MC (2001) Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex. Philos Trans R Soc Lond B Biol Sci 356(1407):299–330. doi:10.1098/rstb.2000.0769

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Buice MA, Cowan JD (2007) Field-theoretic approach to fluctuation effects in neural networks. Phys Rev E Stat Nonlin Soft Matter Phys 75(5 Pt 1):051919

    Article  PubMed  Google Scholar 

  • Camperi M, Wang XJ (1998) A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. J Comput Neurosci 5(4):383–405

    Article  CAS  PubMed  Google Scholar 

  • Durstewitz D, Seamans JK, Sejnowski TJ (2000) Neurocomputational models of working memory. Nat Neurosci 3(Suppl):1184–1191. doi:10.1038/81460

    Article  CAS  PubMed  Google Scholar 

  • Erlhagen W, Schoner G (2002) Dynamic field theory of movement preparation. Psychol Rev 109(3):545–572

    Article  PubMed  Google Scholar 

  • Ermentrout B (1998) Neural networks as spatio-temporal pattern-forming systems. Rep Prog Phys 61(4):353

    Article  Google Scholar 

  • Ermentrout GB, Cowan JD (1979) A mathematical theory of visual hallucination patterns. Biol Cybern 34(3):137–150

    Article  CAS  PubMed  Google Scholar 

  • Hansel D, Sompolinsky H (1998) Modeling feature selectivity in local cortical circuits. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge, MA

    Google Scholar 

  • Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81(10):3088–3092

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Hubel DH, Wiesel TN (1977) Ferrier lecture. Functional architecture of macaque monkey visual cortex. Proc R Soc Lond B Biol Sci 198(1130):1–59

    Article  CAS  PubMed  Google Scholar 

  • Hutt A, Longtin A, Schimansky-Geier L (2008) Additive noise-induced turing transitions in spatial systems with application to neural fields and the swift-hohenberg equation. Phys D Nonlinear Phenom 237(6):755–773

    Article  Google Scholar 

  • Kilpatrick ZP, Bressloff PC (2010) Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Phys D Nonlinear Phenom 239(9):547–560

    Article  Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69

    Article  Google Scholar 

  • Laing CR, Chow CC (2002) A spiking neuron model for binocular rivalry. J Comput Neurosci 12(1):39–53

    Article  PubMed  Google Scholar 

  • McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133

    Article  Google Scholar 

  • Pinto DJ, Brumberg JC, Simons DJ, Ermentrout GB (1996) A quantitative population model of whisker barrels: re-examining the wilson-cowan equations. J Comput Neurosci 3(3):247–264

    Article  CAS  PubMed  Google Scholar 

  • Reichl LE, Prigogine I (1980) A modern course in statistical physics, vol 71. University of Texas Press, Austin

    Google Scholar 

  • Samsonovich A, McNaughton BL (1997) Path integration and cognitive mapping in a continuous attractor neural network model. J Neurosci 17(15):5900–5920

    CAS  PubMed  Google Scholar 

  • Usher M, McClelland JL (2001) The time course of perceptual choice: the leaky, competing accumulator model. Psychol Rev 108(3):550–592

    Article  CAS  PubMed  Google Scholar 

  • Wang XJ (2010) Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev 90(3):1195–1268. doi:10.1152/physrev.00035.2008

    Article  PubMed Central  PubMed  Google Scholar 

  • Wilson HR (2003) Computational evidence for a rivalry hierarchy in vision. Proc Natl Acad Sci USA 100(24):14499–14503. doi:10.1073/pnas.2333622100

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12(1):1–24

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13(2):55–80

    Article  CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Zachary P. Kilpatrick

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  1. Zachary P. Kilpatrick
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Correspondence to Zachary P. Kilpatrick .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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© 2013 Springer Science+Business Media New York

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Kilpatrick, Z.P. (2013). Wilson-Cowan Model. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_80-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_80-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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