{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:23:03Z","timestamp":1758273783276,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T00:00:00Z","timestamp":1653609600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T00:00:00Z","timestamp":1653609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31393\/2017"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31393\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comput Neurosci"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10827-022-00816-w","type":"journal-article","created":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T03:43:11Z","timestamp":1653622991000},"page":"299-311","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Numerical simulations of one- and two-dimensional stochastic neural field equations with delay"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8579-3676","authenticated-orcid":false,"given":"Tiago F.","family":"Sequeira","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6255-3303","authenticated-orcid":false,"given":"Pedro M.","family":"Lima","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,27]]},"reference":[{"key":"816_CR1","doi-asserted-by":"crossref","unstructured":"Amari, S. L. (1977). Dynamics of pattern formation in lateral.inhibition type neural fields. Biological Cybernetics, 27, 77\u201387","DOI":"10.1007\/BF00337259"},{"key":"816_CR2","doi-asserted-by":"publisher","unstructured":"Bell, J., & Cosner, C. (1983). Threshold conditions for a diffusive model of a myelinated axon. Journal of Mathematical Biology 18(1), 39\u201352. https:\/\/doi.org\/10.1007\/BF00275909.","DOI":"10.1007\/BF00275909."},{"key":"816_CR3","doi-asserted-by":"crossref","unstructured":"Bell, J. (1984). Behaviour of some models of myelinated axons. Mathematical Medicine and Biology: A Journal of the IMA 1(2), 149-167. https:\/\/doi.org\/10.1093\/imammb\/1.2.149","DOI":"10.1093\/imammb\/1.2.149"},{"key":"816_CR4","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1162\/089976602317250861","volume":"14","author":"P Bressloff","year":"2002","unstructured":"Bressloff, P., Cowan, J., Golubitsky, M., Thomas, P., & Wiener, M. (2002). What geometric visual hallucinations tell us about the visual cortex. Neural computation, 14, 473\u201391. https:\/\/doi.org\/10.1162\/089976602317250861.","journal-title":"Neural computation"},{"key":"816_CR5","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1007\/BF00275686","volume":"24","author":"H Chi","year":"1986","unstructured":"Chi, H., Bell, J., & Hassard, B. (1986). Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory. Journal of mathematical biology, 24, 583\u2013601. https:\/\/doi.org\/10.1007\/BF00275686.","journal-title":"Journal of mathematical biology"},{"key":"816_CR6","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1111\/j.1467-7687.2008.00769.x","volume":"12","author":"M Clearfield","year":"2009","unstructured":"Clearfield, M., Dineva, E., Smith, L., Diedrich, F., & Thelen, E. (2009). Cue salience and infant perseverative reaching: Tests of the dynamic field theory. Developmental science, 12, 26\u201340b. https:\/\/doi.org\/10.1111\/j.1467-7687.2008.00769.x.","journal-title":"Developmental science"},{"key":"816_CR7","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1016\/j.neuroimage.2010.01.045","volume":"52","author":"S Coombes","year":"2010","unstructured":"Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52, 731\u20139. https:\/\/doi.org\/10.1016\/j.neuroimage.2010.01.045.","journal-title":"NeuroImage"},{"issue":"5","key":"816_CR8","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1016\/0013-4694(80)90006-1","volume":"50","author":"JE Desmedt","year":"1980","unstructured":"Desmedt, J. E., & Cheron, G. (1980). Central somatosensory conduction in man: Neural generators and interpeak latencies of the far-field components recorded from neck and right or left scalp and earlobes. Electroencephalography and Clinical Neurophysiology, 50(5), 382\u2013403. https:\/\/doi.org\/10.1016\/0013-4694(80)90006-1.","journal-title":"Electroencephalography and Clinical Neurophysiology"},{"key":"816_CR9","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1088\/1741-2560\/3\/3\/R02","volume":"3","author":"W Erlhagen","year":"2006","unstructured":"Erlhagen, W., & Bicho, E. (2006). The dynamic neural field approach to cognitive robotics. Journal of neural engineering, 3, 36\u201354. https:\/\/doi.org\/10.1088\/1741-2560\/3\/3\/R02.","journal-title":"Journal of neural engineering"},{"key":"816_CR10","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/j.physd.2010.01.010","volume":"239","author":"G Faye","year":"2010","unstructured":"Faye, G., & Faugeras, O. (2010). Some theoretical and numerical results for delayed neural field equations. Physica D: Nonlinear Phenomena, 239, 561\u2013578. https:\/\/doi.org\/10.1016\/j.physd.2010.01.010.","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"816_CR11","unstructured":"Faye, G., & Faugeras, O. (2010). New results for delayed neural field equations. Cinqui\u00e9me conf\u00e9rence pl\u00e9ni\u00e9re fran\u00e7aise de Neurosciences omputationnelles. Neurocomp, 10"},{"key":"816_CR12","doi-asserted-by":"publisher","first-page":"208107","DOI":"10.1103\/PhysRevLett.95.208107","volume":"95","author":"SE Folias","year":"2005","unstructured":"Folias, S. E., & Bressloff, P. C. (2005). Breathers in two-dimensional neural media. Physical Review Letters, 95, 208107.","journal-title":"Physical Review Letters"},{"key":"816_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1152\/jn.1989.61.2.331","volume":"61","author":"S Funahashi","year":"1989","unstructured":"Funahashi, S., Bruce, C., & Goldman-Rakic, P. S. (1989). Mnemonic coding of visual space in the monkeys dorsolateral prefrontal cortex. Journal of Neurophysiology, 61, 1\u20139. https:\/\/doi.org\/10.1152\/jn.1989.61.2.331.","journal-title":"Journal of Neurophysiology"},{"key":"816_CR14","doi-asserted-by":"crossref","unstructured":"Gerstner, W.,  & Kistler, W. (2002). Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge Univeristy Press, Cambridge.","DOI":"10.1017\/CBO9780511815706"},{"key":"816_CR15","unstructured":"Hahnloser, R., Xie, X., & Seung, H. (2001). A theory of neural integration in the head-direction system. Advances in Neural Information Processing Systems, 14."},{"key":"816_CR16","doi-asserted-by":"crossref","unstructured":"Higham, D. J. (2001). An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review, 43(3), 525-546. https:\/\/doi.org\/10.1137\/S0036144500378302","DOI":"10.1137\/S0036144500378302"},{"key":"816_CR17","doi-asserted-by":"crossref","unstructured":"Hutt, A., & Rougier, N. (2010). Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields. Physical Review E, 82(5), 055701. https:\/\/doi.org\/10.1103\/PhysRevE.82.055701","DOI":"10.1103\/PhysRevE.82.055701"},{"key":"816_CR18","doi-asserted-by":"crossref","unstructured":"Hutt, A., & Rougier, N. (2013). Numerical simulation scheme of one-and two dimensional neural fields involving space-dependent delays. In Neural Fields (pp. 175-185). Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/978-3-642-54593-16","DOI":"10.1007\/978-3-642-54593-1_6"},{"key":"816_CR19","doi-asserted-by":"publisher","unstructured":"Kilpatrick, Z., & Ermentrout, B. (2012). Wandering bumps in stochastic neural fields. SIAM Journal on Applied Dynamical Systems, 12,\u00a0https:\/\/doi.org\/10.1137\/120877106.","DOI":"10.1137\/120877106."},{"key":"816_CR20","doi-asserted-by":"crossref","unstructured":"Kuehn, C. G. &  Riedler, M. (2014). Large deviations for nonlocal stochastic neural fields. Journal of Mathematical Neuroscience 4, 1 (2014). https:\/\/doi.org\/10.1186\/2190-8567-4-1","DOI":"10.1186\/2190-8567-4-1"},{"key":"816_CR21","doi-asserted-by":"publisher","unstructured":"Laing, C. R., Troy, W. C., Gutkin, B., & Ermentrout, G. B. (2002). Multiple bumps in a neuronal model of working memory. SIAM Journal on Applied Mathematics, 63, https:\/\/doi.org\/10.1137\/S0036139901389495","DOI":"10.1137\/S0036139901389495"},{"key":"816_CR22","doi-asserted-by":"publisher","unstructured":"Liley, D., Cadusch, P. J., & Dafilis, M. P. (2009). A spatially continuous mean field theory of electrocortical activity. Network: Computation in Neural Systems, 13,\u00a0https:\/\/doi.org\/10.1088\/0954-898X\/14\/2\/601","DOI":"10.1088\/0954-898X\/14\/2\/601"},{"key":"816_CR23","doi-asserted-by":"crossref","unstructured":"Lima, P. M. (2019). Numerical investigation of stochastic neural field equations. In: Sing, V.K. (ed.).\u00a0Advances in Mathematical Methods and High Performance Computing, 3 51-67. New York.","DOI":"10.1007\/978-3-030-02487-1_2"},{"key":"816_CR24","doi-asserted-by":"crossref","unstructured":"Lund, J., Angelucci, A.,  & Bressloff, P. (2003). Anatomical substrates for functional columns in macaque monkey primary visual cortex. Cerebral cortex (New York, N.Y. : 1991) 13, 15-24. https:\/\/doi.org\/10.1093\/cercor\/13.1.15","DOI":"10.1093\/cercor\/13.1.15"},{"key":"816_CR25","doi-asserted-by":"publisher","first-page":"962","DOI":"10.1137\/15M1022562","volume":"37","author":"P Lima","year":"2015","unstructured":"Lima, P., & Buckwar, E. (2015). Numerical solution of the neural field equation in the two-dimensional case. SIAM Journal on Scientific Computing, 37, 962\u2013979. https:\/\/doi.org\/10.1137\/15M1022562.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"816_CR26","doi-asserted-by":"publisher","first-page":"25","DOI":"10.3389\/fninf.2015.00025","volume":"9","author":"E Nichols","year":"2015","unstructured":"Nichols, E., & Hutt, A. (2015). Neural field simulator: two-dimensional spatio-temporal dynamics involving finite transmission speed. Frontiers in Neuroinformatics, 9, 25. https:\/\/doi.org\/10.3389\/fninf.2015.00025.","journal-title":"Frontiers in Neuroinformatics"},{"key":"816_CR27","doi-asserted-by":"publisher","first-page":"46","DOI":"10.3389\/fpsyg.2013.00046","volume":"4","author":"B Parsons","year":"2013","unstructured":"Parsons, B., Novich, S., & Eagleman, D. (2013). Motor-sensory recalibration modulates perceived simultaneity of cross-modal events at different distances. Frontiers in psychology, 4, 46. https:\/\/doi.org\/10.3389\/fpsyg.2013.00046.","journal-title":"Frontiers in psychology"},{"key":"816_CR28","volume-title":"Neurobiology","author":"GM Shepherd","year":"1994","unstructured":"Shepherd, G. M. (1994). Neurobiology. New York: Oxford University Press."},{"key":"816_CR29","unstructured":"Sequeira, T. (2021). Neuralfieldeq.jl: A flexible solver to compute neural field equations in several scenarios - in press. Journal of Open Source Software."},{"key":"816_CR30","doi-asserted-by":"publisher","unstructured":"Thelen, E., Sch\u00f6ner, G., Scheier, C., & Smith, L. B. (2001). The dynamics of embodiment: A field theory of infant perseverative reaching. Behavioral and Brain Sciences, 24(1), 1\u201334 https:\/\/doi.org\/10.1017\/s0140525x01003910","DOI":"10.1017\/s0140525x01003910"},{"key":"816_CR31","doi-asserted-by":"crossref","unstructured":"Wilson, H., & Cowan, J. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55-80.\u00a0https:\/\/link.springer.com\/article\/10.1007\/BF00288786","DOI":"10.1007\/BF00288786"}],"container-title":["Journal of Computational Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-022-00816-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10827-022-00816-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-022-00816-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T03:26:59Z","timestamp":1656127619000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10827-022-00816-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,27]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["816"],"URL":"https:\/\/doi.org\/10.1007\/s10827-022-00816-w","relation":{},"ISSN":["0929-5313","1573-6873"],"issn-type":[{"type":"print","value":"0929-5313"},{"type":"electronic","value":"1573-6873"}],"subject":[],"published":{"date-parts":[[2022,5,27]]},"assertion":[{"value":"14 September 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}