{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T21:19:01Z","timestamp":1772831941373,"version":"3.50.1"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:p> We develop two algorithms for obtaining an index 1 saddle torus between two attractors of which basin boundary is smooth by using the bisection method. In the first algorithm, which we name \"overall template method\", we make a template approximating a whole attractor and use it for pattern matching. The attractor can be a periodic orbit, a torus and even a chaos. In the second algorithm, which we name \"partial template method\", we make a template approximating only a part of an attractor. In this algorithm, the attractor is restricted to a periodic orbit and a two-torus, but calculation time is much smaller than that of the overall template method. We demonstrate these two algorithms for two solutions, observed in a ring of six-coupled bistable oscillators. One is a saddle torus in the basin boundary of the two switching solutions, and the other is of the two quasi-periodic propagating wave solutions. We calculate the Lyapunov spectrum of the obtained saddle torus, and confirm one positive Lyapunov exponent. <\/jats:p>","DOI":"10.1142\/s0218127413300322","type":"journal-article","created":{"date-parts":[[2013,10,11]],"date-time":"2013-10-11T15:20:00Z","timestamp":1381504800000},"page":"1330032","source":"Crossref","is-referenced-by-count":17,"title":["ALGORITHMS FOR OBTAINING A SADDLE TORUS BETWEEN TWO ATTRACTORS"],"prefix":"10.1142","volume":"23","author":[{"given":"KYOHEI","family":"KAMIYAMA","sequence":"first","affiliation":[{"name":"Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MOTOMASA","family":"KOMURO","sequence":"additional","affiliation":[{"name":"Center for Fundamental Education, Teikyo University of Science, 2525 Yatsusawa, Uenohara-shi, Yamanashi 409-0193, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TETSURO","family":"ENDO","sequence":"additional","affiliation":[{"name":"Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,10,11]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412501234"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412503099"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412300224"},{"key":"p_4","first-page":"1250310","volume":"22","author":"Kamiyama K.","year":"2012","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1984.1085495"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407017732"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300024"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.61.1605"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1587\/nolta.2.139"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413300322","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:43:23Z","timestamp":1565099003000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413300322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":9,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2013,10,11]]},"published-print":{"date-parts":[[2013,9]]}},"alternative-id":["10.1142\/S0218127413300322"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413300322","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}