{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:47:47Z","timestamp":1753886867468,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T00:00:00Z","timestamp":1529884800000},"content-version":"vor","delay-in-days":175,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>A 3D fractional\u2010order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is <jats:italic>q<\/jats:italic> \u2265 0.8477. The fractional\u2010order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order <jats:italic>q<\/jats:italic> is given. Furthermore, there are the coexisting \u201cpositive attractor\u201d and \u201cnegative attractor\u201d in this fractional\u2010order chaotic system, and the necessary condition for \u201cpositive attractor\u201d and \u201cnegative attractor\u201d is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid.<\/jats:p>","DOI":"10.1155\/2018\/4192824","type":"journal-article","created":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T23:31:55Z","timestamp":1529969515000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Fractional\u2010Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0079-1004","authenticated-orcid":false,"given":"Ping","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meihua","family":"Ke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,6,25]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1142\/3033"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198508397.001.0001"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3170-x"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3808-3"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3542-x"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/4037682"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-2870-6"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-015-0056-5"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2364-y"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1142\/3779"},{"volume-title":"Fractional Differential Equations","year":"1999","author":"Podlubny I.","key":"e_1_2_8_11_2"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3546-6"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2172-4"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/81.404062"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/21\/10\/100505"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1177\/0959651813492326"},{"key":"e_1_2_8_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2007.05.081"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.013"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2012.2206936"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/4192824.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/4192824.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2018\/4192824","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T23:10:06Z","timestamp":1723158606000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2018\/4192824"}},"subtitle":[],"editor":[{"given":"Viet-Thanh","family":"Pham","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1155\/2018\/4192824"],"URL":"https:\/\/doi.org\/10.1155\/2018\/4192824","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"2018-03-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-04-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-06-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"4192824"}}