{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:41:36Z","timestamp":1761597696411},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> The Nagumo\u2013Sato model is a simple mathematical expression of a single neuron, and it is categorized as a discrete-time hybrid dynamical system. To compute bifurcation sets in such a discrete-time hybrid dynamical system accurately, conditions for periodic solutions and bifurcations are formulated herewith as a boundary value problem, and Newton\u2019s method is implemented to solve that problem. As the results of the analysis, the following properties are obtained: border-collision bifurcations play a dominant role in dynamical behavior of the model; chaotic regions are distinguished by tangent bifurcations; and multistable attractors are observed in its coupled system. We demonstrate several bifurcation diagrams and corresponding topological properties of periodic solutions. <\/jats:p>","DOI":"10.1142\/s0218127416300068","type":"journal-article","created":{"date-parts":[[2016,4,6]],"date-time":"2016-04-06T03:23:16Z","timestamp":1459912996000},"page":"1630006","source":"Crossref","is-referenced-by-count":2,"title":["Bifurcation Analysis of the Nagumo\u2013Sato Model and Its Coupled Systems"],"prefix":"10.1142","volume":"26","author":[{"given":"Daisuke","family":"Ito","sequence":"first","affiliation":[{"name":"Department of Electronic Systems Engineering, The University of Shiga Prefecture, 2500 Hassaka-cho, Hikone-shi, Shiga 522-8533, Japan"}]},{"given":"Tetsushi","family":"Ueta","sequence":"additional","affiliation":[{"name":"Center for Administration of Information Technology, Tokushima University, 2-1 Minami-Jousanjima, Tokushima-shi, Tokushima 770-8501, Japan"}]},{"given":"Takuji","family":"Kousaka","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Energy Systems Engineering, Oita University, 700 Dannoharu, Oita-shi, Oita 870-1192, Japan"}]},{"given":"Kazuyuki","family":"Aihara","sequence":"additional","affiliation":[{"name":"Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo 152-8505, Japan"}]}],"member":"219","published-online":{"date-parts":[[2016,4,5]]},"reference":[{"key":"S0218127416300068BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(90)90136-C"},{"key":"S0218127416300068BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/81.841921"},{"key":"S0218127416300068BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00178-2"},{"key":"S0218127416300068BIB004","volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"Bernardo M.","year":"2008"},{"key":"S0218127416300068BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00175-7"},{"key":"S0218127416300068BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01207252"},{"key":"S0218127416300068BIB007","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.60.2715"},{"key":"S0218127416300068BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2004.01.036"},{"key":"S0218127416300068BIB009","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1215\/kjm\/1250521865","volume":"22","author":"Hata M.","year":"1982","journal-title":"J. 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