{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:18:22Z","timestamp":1649063902936},"reference-count":18,"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":[[2011,9]]},"abstract":"<jats:p> This paper considers a class of three-dimensional systems constructed by rotating some planar symmetric polynomial vector fields. It shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on a family of invariant torus. For two three-dimensional systems, exact explicit parametric representations of the knotted periodic orbits are given. For their perturbed systems, the chaotic behavior is discussed by using two different methods. <\/jats:p>","DOI":"10.1142\/s0218127411029896","type":"journal-article","created":{"date-parts":[[2011,11,17]],"date-time":"2011-11-17T11:39:00Z","timestamp":1321529940000},"page":"2505-2523","source":"Crossref","is-referenced-by-count":3,"title":["KNOTTED PERIODIC ORBITS AND CHAOTIC BEHAVIOR OF A CLASS OF THREE-DIMENSIONAL FLOWS"],"prefix":"10.1142","volume":"21","author":[{"given":"JIBIN","family":"LI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FENGJUAN","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004152"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(83)90045-9"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/020\/718132"},{"key":"rf4","first-page":"1049","volume":"13","author":"Bulgakov V. I.","journal-title":"Diff. Eqs."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-003-1031-4"},{"key":"rf6","author":"Chen F. J.","journal-title":"American J. Math."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1985-0797057-1"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496000448"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(97)00094-5"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/11\/4\/021"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf12","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF00250717","volume":"90","author":"Holmes P.","journal-title":"Arch. Rat. Mech. Anal."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(86)90076-X"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(89)90026-2"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023639"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.2307\/2321909"},{"key":"rf17","first-page":"994","volume":"17","author":"Rozet I. G.","journal-title":"Diff. Eqs."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00264-3"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127411029896","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:37:19Z","timestamp":1565131039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127411029896"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9]]},"references-count":18,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2011,9]]}},"alternative-id":["10.1142\/S0218127411029896"],"URL":"https:\/\/doi.org\/10.1142\/s0218127411029896","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9]]}}}