{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,26]],"date-time":"2023-03-26T22:54:32Z","timestamp":1679871272839},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p> The Muthuswamy\u2013Chua system [Formula: see text] describes the simplest electronic circuit which can have chaotic phenomena. In this paper, we first prove the existence of three families of consecutive periodic orbits of the system when \u03b1 = 0, two of which are located on consecutive invariant surfaces and form two invariant topological cylinders. Then we prove that for \u03b1 &gt; 0 if the system has a periodic orbit or a chaotic attractor, it must intersect both of the planes z = 0 and z = -1 infinitely many times as t tends to infinity. As a byproduct, we get an example of unstable invariant topological cylinders which are not normally hyperbolic and which are also destroyed under small perturbations. <\/jats:p>","DOI":"10.1142\/s0218127413501368","type":"journal-article","created":{"date-parts":[[2013,9,18]],"date-time":"2013-09-18T07:08:56Z","timestamp":1379488136000},"page":"1350136","source":"Crossref","is-referenced-by-count":9,"title":["DYNAMICS OF THE MUTHUSWAMY\u2013CHUA SYSTEM"],"prefix":"10.1142","volume":"23","author":[{"given":"YUANFAN","family":"ZHANG","sequence":"first","affiliation":[{"name":"UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XIANG","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,9,18]]},"reference":[{"key":"p_2","first-page":"52","volume":"157","author":"Coppel W. A.","year":"1987","journal-title":"Pitman Res. Notes Math."},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(91)90054-D"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1063\/1.2897983"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2008.10.011"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2010.01.007"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.10.019"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1142\/S1402925112500295"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027076"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413501368","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:51:13Z","timestamp":1565117473000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413501368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":8,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2013,9,17]]},"published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.1142\/S0218127413501368"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413501368","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8]]}}}