{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:01:02Z","timestamp":1772290862263,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> The Nagumo\u2013Sato (NS) model is a one-dimensional piecewise linear map that describes simplified dynamics of a single neuron. The NS model and its network extension, coupled Nagumo\u2013Sato models, exhibit complex behavior both in their transient dynamics and after converging to periodic orbits. However, the way the period and the transient length change against the parameters is not completely understood. In this study, we numerically investigate the transient and periodic dynamics in single and coupled NS models. Simulation results indicate the following observations. (1) The period of a single NS model shows layered structures associated with the Farey sequence. (2) Two coupled NS models show discontinuity in the transient length, even though the period does not change. (3) In the case of an associative memory model consisting of NS models, there exists a small parameter region where both the period and the transient length increase considerably. The dynamics within the region is much more complex than that outside the region. <\/jats:p>","DOI":"10.1142\/s0218127412300212","type":"journal-article","created":{"date-parts":[[2012,4,23]],"date-time":"2012-04-23T21:04:26Z","timestamp":1335215066000},"page":"1230021","source":"Crossref","is-referenced-by-count":4,"title":["NUMERICAL ANALYSIS OF TRANSIENT AND PERIODIC DYNAMICS IN SINGLE AND COUPLED NAGUMO\u2013SATO MODELS"],"prefix":"10.1142","volume":"22","author":[{"given":"MAKITO","family":"OKU","sequence":"first","affiliation":[{"name":"Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KAZUYUKI","family":"AIHARA","sequence":"additional","affiliation":[{"name":"Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,7,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(96)00061-5"},{"key":"rf2","unstructured":"K.\u00a0Aihara, Bifurcation Phenomena in Nonlinear Systems and Theory of Dynamical Systems, ed. H.\u00a0Kawakami (World Scientific, Singapore, 1990)\u00a0pp. 143\u2013161."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(90)90136-C"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2010.0237"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(72)90075-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1063\/1.881047"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5193(61)90046-7"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.60.2715"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01010333"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023271109747"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00290179"},{"key":"rf13","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1215\/kjm\/1250521865","volume":"22","author":"Hata M.","journal-title":"J. Math. Kyoto Univ."},{"key":"rf14","volume-title":"Chaos in Neural Network Models","author":"Hata M.","year":"1998"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.79.8.2554"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1063\/1.166254"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.74.1033"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(90)90534-U"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1063\/1.3212934"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002266"},{"key":"rf22","first-page":"353","volume":"21","author":"Kohonen T.","journal-title":"IEEE Trans. Comput. C"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/BF03168579"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/BF00290514"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1972.4309133"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/22\/8\/003"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.64.1138"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(81)90624-1"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80029-2"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1021\/j100054a001"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412300212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:32:07Z","timestamp":1565098327000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412300212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":28,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,7,16]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S0218127412300212"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412300212","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}