Malo, Jesús; Esteve-Taboada, José Juan; Bertalmío, Marcelo Cortical divisive normalization from Wilson-Cowan neural dynamics. (English) Zbl 07812571 J. Nonlinear Sci. 34, No. 2, Paper No. 35, 36 p. (2024). MSC: 92B20 91E30 35Q92 PDFBibTeX XMLCite \textit{J. Malo} et al., J. Nonlinear Sci. 34, No. 2, Paper No. 35, 36 p. (2024; Zbl 07812571) Full Text: DOI arXiv OA License
Thieu, Thi Kim Thoa; Muntean, Adrian; Melnik, Roderick Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications. (English) Zbl 07782417 Math. Methods Appl. Sci. 46, No. 6, 7368-7390 (2023). MSC: 60H10 60H35 92B05 PDFBibTeX XMLCite \textit{T. K. T. Thieu} et al., Math. Methods Appl. Sci. 46, No. 6, 7368--7390 (2023; Zbl 07782417) Full Text: DOI arXiv
Painchaud, Vincent; Doyon, Nicolas; Desrosiers, Patrick Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition. (English) Zbl 1508.92012 Biol. Cybern. 116, No. 5-6, 527-543 (2022). MSC: 92B20 60J28 PDFBibTeX XMLCite \textit{V. Painchaud} et al., Biol. Cybern. 116, No. 5--6, 527--543 (2022; Zbl 1508.92012) Full Text: DOI arXiv
Winkler, Marius; Dumont, Grégory; Schöll, Eckehard; Gutkin, Boris Phase response approaches to neural activity models with distributed delay. (English) Zbl 1491.92027 Biol. Cybern. 116, No. 2, 191-203 (2022). MSC: 92B20 92B25 PDFBibTeX XMLCite \textit{M. Winkler} et al., Biol. Cybern. 116, No. 2, 191--203 (2022; Zbl 1491.92027) Full Text: DOI
Kaslik, Eva; Kokovics, Emanuel-Attila; Rădulescu, Anca Stability and bifurcations in Wilson-Cowan systems with distributed delays, and an application to basal ganglia interactions. (English) Zbl 1478.37089 Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 105984, 24 p. (2022). MSC: 37N25 45G15 92D30 PDFBibTeX XMLCite \textit{E. Kaslik} et al., Commun. Nonlinear Sci. Numer. Simul. 104, Article ID 105984, 24 p. (2022; Zbl 1478.37089) Full Text: DOI arXiv
Akhmet, Marat; Çağ, Sabahattin Bifurcation analysis of Wilson-Cowan model with singular impulses. (English) Zbl 1492.37081 Discontin. Nonlinearity Complex. 10, No. 1, 161-172 (2021). MSC: 37N25 37M20 34K18 92D25 PDFBibTeX XMLCite \textit{M. Akhmet} and \textit{S. Çağ}, Discontin. Nonlinearity Complex. 10, No. 1, 161--172 (2021; Zbl 1492.37081) Full Text: DOI arXiv
Asswad, Rand; Boscain, Ugo; Turco, Giuseppina; Prandi, Dario; Sacchelli, Ludovic An auditory cortex model for sound processing. (English) Zbl 1486.92007 Nielsen, Frank (ed.) et al., Geometric science of information. 5th international conference, GSI 2021, Paris, France, July 21–23, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12829, 56-64 (2021). MSC: 92B20 45J05 PDFBibTeX XMLCite \textit{R. Asswad} et al., Lect. Notes Comput. Sci. 12829, 56--64 (2021; Zbl 1486.92007) Full Text: DOI arXiv
Wilson, Hugh R.; Cowan, Jack D. Evolution of the Wilson-Cowan equations. (English) Zbl 1480.92020 Biol. Cybern. 115, No. 6, 643-653 (2021). MSC: 92B20 35Q92 91E30 91E40 PDFBibTeX XMLCite \textit{H. R. Wilson} and \textit{J. D. Cowan}, Biol. Cybern. 115, No. 6, 643--653 (2021; Zbl 1480.92020) Full Text: DOI
Kaslik, Eva; Kokovics, Emanuel-Attila; Rădulescu, Anca Wilson-Cowan neuronal interaction models with distributed delays. (English) Zbl 1482.92019 Lacarbonara, Walter (ed.) et al., New trends in nonlinear dynamics. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17–20, 2019. Volume III. Cham: Springer. 203-211 (2020). Reviewer: Angela Slavova (Sofia) MSC: 92B20 34K25 34K18 34K23 PDFBibTeX XMLCite \textit{E. Kaslik} et al., in: New trends in nonlinear dynamics. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17--20, 2019. Volume III. Cham: Springer. 203--211 (2020; Zbl 1482.92019) Full Text: DOI
Kaslik, Eva; Mureşan, Raluca Dynamics of a homeostatically regulated neural system with delayed connectivity. (English) Zbl 1482.92020 Lacarbonara, Walter (ed.) et al., New trends in nonlinear dynamics. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17–20, 2019. Volume III. Cham: Springer. 173-182 (2020). Reviewer: Angela Slavova (Sofia) MSC: 92B20 34K18 34K25 PDFBibTeX XMLCite \textit{E. Kaslik} and \textit{R. Mureşan}, in: New trends in nonlinear dynamics. Proceedings of the first international nonlinear dynamics conference, NODYCON 2019, Rome, Italy, February 17--20, 2019. Volume III. Cham: Springer. 173--182 (2020; Zbl 1482.92020) Full Text: DOI
Liang, Conggang; Zhang, Houchao; Shi, Dongyang Convergence analysis of Wilson element for a generalized nerve conduction equation. (Chinese. English summary) Zbl 1463.65300 J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 212-218 (2020). MSC: 65M60 65N30 65N12 92C20 35Q92 65M20 PDFBibTeX XMLCite \textit{C. Liang} et al., J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 212--218 (2020; Zbl 1463.65300) Full Text: DOI
Pérez-Cervera, Alberto; Seara, Tere M.; Huguet, Gemma Phase-locked states in oscillating neural networks and their role in neural communication. (English) Zbl 1451.92026 Commun. Nonlinear Sci. Numer. Simul. 80, Article ID 104992, 20 p. (2020). MSC: 92B20 PDFBibTeX XMLCite \textit{A. Pérez-Cervera} et al., Commun. Nonlinear Sci. Numer. Simul. 80, Article ID 104992, 20 p. (2020; Zbl 1451.92026) Full Text: DOI arXiv
Moeinzadeh, Hossein; Assad, Joseph; Bifulco, Paolo; Cesarelli, Mario; Mcewan, Alistair L.; O’Loughlin, Aiden; Shugman, Ibrahim M.; Tapson, Jonathan C.; Thiagalingam, Aravinda; Gargiulo, Gaetano D. Unipolar cardiac leads between history and science. (English) Zbl 1444.92055 Naik, Ganesh (ed.), Biomedical signal processing. Advances in theory, algorithms and applications. Singapore: Springer. Ser. BioEng., 203-224 (2020). MSC: 92C55 PDFBibTeX XMLCite \textit{H. Moeinzadeh} et al., in: Biomedical signal processing. Advances in theory, algorithms and applications. Singapore: Springer. 203--224 (2020; Zbl 1444.92055) Full Text: DOI
Duchet, Benoit; Weerasinghe, Gihan; Cagnan, Hayriye; Brown, Peter; Bick, Christian; Bogacz, Rafal Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model. (English) Zbl 1443.92047 J. Math. Neurosci. 10, Paper No. 4, 39 p. (2020). MSC: 92B20 92C50 92C20 PDFBibTeX XMLCite \textit{B. Duchet} et al., J. Math. Neurosci. 10, Paper No. 4, 39 p. (2020; Zbl 1443.92047) Full Text: DOI
Conti, Federica; Van Gorder, Robert A. The role of network structure and time delay in a metapopulation Wilson-Cowan model. (English) Zbl 1416.92007 J. Theor. Biol. 477, 1-13 (2019). MSC: 92B20 05C90 PDFBibTeX XMLCite \textit{F. Conti} and \textit{R. A. Van Gorder}, J. Theor. Biol. 477, 1--13 (2019; Zbl 1416.92007) Full Text: DOI
Ahmadizadeh, Saeed; Nešić, Dragan; Freestone, Dean R.; Grayden, David B. On synchronization of networks of Wilson-Cowan oscillators with diffusive coupling. (English) Zbl 1343.93004 Automatica 71, 169-178 (2016). MSC: 93A14 93C15 93C10 92B20 PDFBibTeX XMLCite \textit{S. Ahmadizadeh} et al., Automatica 71, 169--178 (2016; Zbl 1343.93004) Full Text: DOI
Cowan, Jack D.; Neuman, Jeremy; van Drongelen, Wim Wilson-Cowan equations for neocortical dynamics. (English) Zbl 1356.92016 J. Math. Neurosci. 6, Paper No. 1, 24 p. (2016). MSC: 92C20 PDFBibTeX XMLCite \textit{J. D. Cowan} et al., J. Math. Neurosci. 6, Paper No. 1, 24 p. (2016; Zbl 1356.92016) Full Text: DOI
Greenwood, Priscilla E.; Ward, Lawrence M. Stochastic neuron models. (English) Zbl 1342.92007 Mathematical Biosciences Institute Lecture Series. Stochastics in Biological Systems 1.5. Cham: Springer (ISBN 978-3-319-26909-2/pbk; 978-3-319-26911-5/ebook). x, 75 p. (2016). Reviewer: Carlo Laing (Auckland) MSC: 92-02 92B20 92C20 92B25 37A50 60H10 PDFBibTeX XMLCite \textit{P. E. Greenwood} and \textit{L. M. Ward}, Stochastic neuron models. Cham: Springer (2016; Zbl 1342.92007) Full Text: DOI
Negahbani, Ehsan; Steyn-Ross, D. Alistair; Steyn-Ross, Moira L.; Wilson, Marcus T.; Sleigh, Jamie W. Noise-induced precursors of state transitions in the stochastic Wilson-Cowan model. (English) Zbl 1357.92015 J. Math. Neurosci. 5, Paper No. 9, 27 p. (2015). MSC: 92C20 PDFBibTeX XMLCite \textit{E. Negahbani} et al., J. Math. Neurosci. 5, Paper No. 9, 27 p. (2015; Zbl 1357.92015) Full Text: DOI
Harris, Jeremy; Ermentrout, Bard Bifurcations in the Wilson-Cowan equations with nonsmooth firing rate. (English) Zbl 1321.34062 SIAM J. Appl. Dyn. Syst. 14, No. 1, 43-72 (2015). MSC: 34C60 34A60 92B20 92C20 34A36 34C23 PDFBibTeX XMLCite \textit{J. Harris} and \textit{B. Ermentrout}, SIAM J. Appl. Dyn. Syst. 14, No. 1, 43--72 (2015; Zbl 1321.34062) Full Text: DOI
Cowan, Jack A personal account of the development of the field theory of large-scale brain activity from 1945 onward. (English) Zbl 1462.92013 Coombes, Stephen (ed.) et al., Neural fields. Theory and applications. Berlin: Springer. 47-96 (2014). MSC: 92B20 PDFBibTeX XMLCite \textit{J. Cowan}, in: Neural fields. Theory and applications. Berlin: Springer. 47--96 (2014; Zbl 1462.92013) Full Text: DOI
Maruyama, Yuya; Kakimoto, Yuta; Araki, Osamu Analysis of chaotic oscillations induced in two coupled Wilson-Cowan models. (English) Zbl 1294.92010 Biol. Cybern. 108, No. 3, 355-363 (2014). MSC: 92C20 37N25 PDFBibTeX XMLCite \textit{Y. Maruyama} et al., Biol. Cybern. 108, No. 3, 355--363 (2014; Zbl 1294.92010) Full Text: DOI
Wang, Pingli; Shi, Dongyang A superconvergence analysis and extrapolations of nonconforming quasi-Wilson element to the generalized nerve conductive equations. (Chinese. English summary) Zbl 1313.65274 J. Biomath. 28, No. 4, 672-680 (2013). MSC: 65M60 92C20 35Q92 65M12 65M20 65M15 PDFBibTeX XMLCite \textit{P. Wang} and \textit{D. Shi}, J. Biomath. 28, No. 4, 672--680 (2013; Zbl 1313.65274)
Merrison-Hort, Robert; Yousif, Nada; Njap, Felix; Hofmann, Ulrich G.; Burylko, Oleksandr; Borisyuk, Roman An interactive channel model of the basal ganglia: bifurcation analysis under healthy and Parkinsonian conditions. (English) Zbl 1291.92041 J. Math. Neurosci. 3, Paper No. 14, 29 p. (2013). MSC: 92C20 PDFBibTeX XMLCite \textit{R. Merrison-Hort} et al., J. Math. Neurosci. 3, Paper No. 14, 29 p. (2013; Zbl 1291.92041) Full Text: DOI
Riedler, Martin G.; Buckwar, Evelyn Laws of large numbers and Langevin approximations for stochastic neural field equations. (English) Zbl 1295.60030 J. Math. Neurosci. 3, Paper No. 1, 54 p. (2013). MSC: 60F05 60J25 60J75 92C20 PDFBibTeX XMLCite \textit{M. G. Riedler} and \textit{E. Buckwar}, J. Math. Neurosci. 3, Paper No. 1, 54 p. (2013; Zbl 1295.60030) Full Text: DOI arXiv
Xie, Shasha; Huang, Zhenkun Almost periodic solutions for Wilson-Cowan type model with time-varying delays. (English) Zbl 1264.34086 Discrete Dyn. Nat. Soc. 2013, Article ID 683091, 7 p. (2013). MSC: 34C27 93D05 92B20 PDFBibTeX XMLCite \textit{S. Xie} and \textit{Z. Huang}, Discrete Dyn. Nat. Soc. 2013, Article ID 683091, 7 p. (2013; Zbl 1264.34086) Full Text: DOI
Burke, John; Desroches, Mathieu; Barry, Anna M.; Kaper, Tasso J.; Kramer, Mark A. A showcase of torus canards in neuronal bursters. (English) Zbl 1291.92025 J. Math. Neurosci. 2, Paper No. 3, 30 p. (2012). MSC: 92C20 34E17 34C23 37G15 PDFBibTeX XMLCite \textit{J. Burke} et al., J. Math. Neurosci. 2, Paper No. 3, 30 p. (2012; Zbl 1291.92025) Full Text: DOI arXiv
Folias, Stefanos E.; Ermentrout, G. Bard Bifurcations of stationary solutions in an interacting pair of E-I neural fields. (English) Zbl 1276.37049 SIAM J. Appl. Dyn. Syst. 11, No. 3, 895-938 (2012). Reviewer: Carsten Conradi (Magdeburg) MSC: 37N25 92B20 35B36 47N20 34K21 37G35 35Q92 PDFBibTeX XMLCite \textit{S. E. Folias} and \textit{G. B. Ermentrout}, SIAM J. Appl. Dyn. Syst. 11, No. 3, 895--938 (2012; Zbl 1276.37049) Full Text: DOI Link
Søndergaard, Peter L.; Torrésani, Bruno; Balazs, Peter The linear time frequency analysis toolbox. (English) Zbl 1270.65083 Int. J. Wavelets Multiresolut. Inf. Process. 10, No. 4, 1250032, 27 p. (2012). Reviewer: Alla Boikova (Penza) MSC: 65T40 42A10 42-04 65T50 94A12 92C55 PDFBibTeX XMLCite \textit{P. L. Søndergaard} et al., Int. J. Wavelets Multiresolut. Inf. Process. 10, No. 4, 1250032, 27 p. (2012; Zbl 1270.65083) Full Text: DOI
Decker, R.; Noonburg, V. W. A periodically forced Wilson-Cowan system with multiple attractors. (English) Zbl 1318.92005 SIAM J. Math. Anal. 44, No. 2, 887-905 (2012). MSC: 92B20 34C25 37G15 34C07 PDFBibTeX XMLCite \textit{R. Decker} and \textit{V. W. Noonburg}, SIAM J. Math. Anal. 44, No. 2, 887--905 (2012; Zbl 1318.92005) Full Text: DOI
Touboul, Jonathan D.; Ermentrout, G. Bard Finite-size and correlation-induced effects in mean-field dynamics. (English) Zbl 1446.92086 J. Comput. Neurosci. 31, No. 3, 453-484 (2011). MSC: 92B20 PDFBibTeX XMLCite \textit{J. D. Touboul} and \textit{G. B. Ermentrout}, J. Comput. Neurosci. 31, No. 3, 453--484 (2011; Zbl 1446.92086) Full Text: arXiv
Folias, Stefanos E. Nonlinear analysis of breathing pulses in a synaptically coupled neural network. (English) Zbl 1219.92008 SIAM J. Appl. Dyn. Syst. 10, No. 2, 744-787 (2011). MSC: 92C20 65C20 37N25 92B20 PDFBibTeX XMLCite \textit{S. E. Folias}, SIAM J. Appl. Dyn. Syst. 10, No. 2, 744--787 (2011; Zbl 1219.92008) Full Text: DOI
Roxin, Alex; Montbrió, Ernest How effective delays shape oscillatory dynamics in neuronal networks. (English) Zbl 1213.37127 Physica D 240, No. 3, 323-345 (2011). Reviewer: Xueyong Zhou (Xinyang) MSC: 37N25 92B20 34C25 PDFBibTeX XMLCite \textit{A. Roxin} and \textit{E. Montbrió}, Physica D 240, No. 3, 323--345 (2011; Zbl 1213.37127) Full Text: DOI arXiv
Coombes, Stephen; Laing, Carlo Delays in activity-based neural networks. (English) Zbl 1185.92003 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1891, 1117-1129 (2009). MSC: 92B20 92C20 PDFBibTeX XMLCite \textit{S. Coombes} and \textit{C. Laing}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1891, 1117--1129 (2009; Zbl 1185.92003) Full Text: DOI
Yousif, Nada; Denham, Mike The role of cortical feedback in the generation of the temporal receptive field responses of lateral geniculate nucleus neurons: a computational modelling study. (English) Zbl 1125.92018 Biol. Cybern. 97, No. 4, 269-277 (2007). MSC: 92C20 PDFBibTeX XMLCite \textit{N. Yousif} and \textit{M. Denham}, Biol. Cybern. 97, No. 4, 269--277 (2007; Zbl 1125.92018) Full Text: DOI
Noonburg, V. W. Non-homogeneous Wilson-Cowan model. (English) Zbl 1050.92010 Nonlinear Stud. 11, No. 3, 481-490 (2004). MSC: 92C20 34C25 92B20 37G15 PDFBibTeX XMLCite \textit{V. W. Noonburg}, Nonlinear Stud. 11, No. 3, 481--490 (2004; Zbl 1050.92010)
Ueta, Tetsushi; Chen, Guanrong On synchronization and control of coupled Wilson-Cowan neural oscillators. (English) Zbl 1077.34040 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 1, 163-175 (2003). Reviewer: Sergiy Yanchuk (Berlin) MSC: 34C15 34C28 92B20 34C25 34D20 34D05 PDFBibTeX XMLCite \textit{T. Ueta} and \textit{G. Chen}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 1, 163--175 (2003; Zbl 1077.34040) Full Text: DOI
Noonburg, V. W.; Benardete, D.; Pollina, B. A periodically forced Wilson–Cowan system. (English) Zbl 1035.92007 SIAM J. Appl. Math. 63, No. 5, 1585-1603 (2003). MSC: 92C20 92B20 34C25 37G15 34C60 37N25 PDFBibTeX XMLCite \textit{V. W. Noonburg} et al., SIAM J. Appl. Math. 63, No. 5, 1585--1603 (2003; Zbl 1035.92007) Full Text: DOI
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Khibnik, Alexander I.; Borisyuk, Roman M.; Roose, Dirk Numerical bifurcation analysis of a model of coupled neural oscillators. (English) Zbl 0755.92003 Bifurcation and symmetry. Cross influence between mathematics and applications, Proc. Workshop, Marburg/Ger. 1991, ISNM 104, 215-228 (1992). MSC: 92B20 65L99 92-08 PDFBibTeX XMLCite \textit{A. I. Khibnik} et al., in: Bifurcation and symmetry. Cross influence between mathematics and applications. Proceedings of a workshop, held Marburg, Germany, June, 2- 14, 1991. Basel etc.: Birkhäuser Verlag. 215--228 (1992; Zbl 0755.92003)
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