{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T22:18:40Z","timestamp":1648937920806},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> In this study, we investigate the bifurcation of the quasi-periodic solution in a ring of three-coupled, bistable oscillators. The quasi-periodic solution under study is a propagating wave solution with three-phase synchronized envelope, and we name it \"ICC3\u03d5\" which means invariant closed curve for which time waveforms have three-phase synchronized envelope. We obtain the two-parameter bifurcation diagram of ICC3\u03d5 with respect to the coupling factor \u03b1 versus the nonlinear strength \u03f5. Consequently, we detect several Arnold tongues showing various periodic solutions of ICC3\u03d5. By investigating the bifurcation on the boundary of these Arnold tongues, we clarify the transition from periodic to quasi-periodic solution of ICC3\u03d5 or the inverse. Specifically, the transition of the period-4, period-5, and period-7 solutions to ICC3\u03d5 is due to a saddle-node bifurcation, which has no hysteresis. In contrast, the transition from the period-3 solution to ICC3\u03d5 is a combination of subcritical pitchfork and heteroclinic bifurcations; hence, it has hysteresis. We draw diagrams showing the connection of unstable manifolds of heteroclinic bifurcation. <\/jats:p>","DOI":"10.1142\/s0218127412503087","type":"journal-article","created":{"date-parts":[[2013,1,15]],"date-time":"2013-01-15T06:54:47Z","timestamp":1358232887000},"page":"1250308","source":"Crossref","is-referenced-by-count":0,"title":["BIFURCATION ANALYSIS OF THE QUASI-PERIODIC SOLUTION WITH THREE-PHASE SYNCHRONIZED ENVELOPES IN A RING OF THREE-COUPLED, BISTABLE OSCILLATORS"],"prefix":"10.1142","volume":"22","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":[[2013,1,14]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/1022003"},{"key":"rf2","first-page":"559","volume":"86","author":"Aruga Y.","year":"2003","journal-title":"IEICE Trans. A"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412501234"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1137\/0147038"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/040608714"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1093\/ietfec\/e91-a.9.2540"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1587\/nolta.2.139"},{"key":"rf10","first-page":"2233","volume":"87","author":"Yamauchi M.","year":"2004","journal-title":"IEICE Trans. Fund. E"},{"key":"rf11","first-page":"1811","volume":"75","author":"Yoshinaga T.","year":"1992","journal-title":"IEICE Trans. A"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412503087","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:25:53Z","timestamp":1565133953000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412503087"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":10,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2013,1,14]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S0218127412503087"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412503087","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}