{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T08:57:15Z","timestamp":1649149035217},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,4]]},"abstract":"<jats:p> In this paper, we consider a switching system modeled by a discrete-time flow model, which has piecewise linear dynamics. In the system, it has been known that aperiodic oscillations occur. We qualitatively classify behaviors of the system into three modes, and define \"blocks\" consisting of the modes. We define a kind of Poincar\u00e9 map by using the blocks, and show that the system has an invariant region in the Poincar\u00e9 map. Moreover, we show that the Poincar\u00e9 map can be reduced to a one-dimensional map. Finally, applying Lasota\u2013Yorke's theorem to the one-dimensional map, we prove that the aperiodic oscillation is chaotic. <\/jats:p>","DOI":"10.1142\/s0218127403007023","type":"journal-article","created":{"date-parts":[[2003,6,17]],"date-time":"2003-06-17T12:04:14Z","timestamp":1055851454000},"page":"981-994","source":"Crossref","is-referenced-by-count":3,"title":["ANALYSIS OF APERIODIC OSCILLATIONS IN A FLOW MODEL OF A SWITCHING SYSTEM"],"prefix":"10.1142","volume":"13","author":[{"given":"HIROTO","family":"TANAKA","sequence":"first","affiliation":[{"name":"Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8351, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TOSHIMITSU","family":"USHIO","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8351, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/49.68444"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1973-0335758-1"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/90.282603"},{"key":"rf7","first-page":"734","volume":"85","author":"Tanaka H.","journal-title":"IEICE Trans. Fundamentals E"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:13:34Z","timestamp":1565136814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":4,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,4]]}},"alternative-id":["10.1142\/S0218127403007023"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007023","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}