{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T04:25:32Z","timestamp":1648527932008},"reference-count":45,"publisher":"World Scientific Pub Co Pte Lt","issue":"13","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501216"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,15]]},"abstract":" Little seems to be known about the chaotification problem in the framework of fractional order nonlinear systems. Based on the negative damping instability mechanism and fractional calculus technique, this paper reports the onset of chaos in fractional order Lorenz system with periodic system parameters via asymptotically period-doubling cascade. To further understand the complex dynamics of the system, some basic properties such as the largest Lyapunov exponents, bifurcation diagram, routes to chaos, asymptotically periodic windows, possible chaotic and asymptotically periodic window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations. Of particular interest is a striking finding that fractional derivative can chaotify the globally stable periodic system without feedback control. <\/jats:p>","DOI":"10.1142\/s0218127417502078","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T03:03:43Z","timestamp":1514948623000},"page":"1750207","source":"Crossref","is-referenced-by-count":2,"title":["The Onset of Chaos via Asymptotically Period-Doubling Cascade in Fractional Order Lorenz System"],"prefix":"10.1142","volume":"27","author":[{"given":"Xiaofang","family":"Lin","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"}]},{"given":"Binghui","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-7589-2865","authenticated-orcid":false,"given":"Caibin","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2018,1,3]]},"reference":[{"key":"S0218127417502078BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.03.022"},{"key":"S0218127417502078BIB002","first-page":"1","volume":"20","author":"Burton T. A.","year":"2013","journal-title":"Dyn. Cont. Discr. Impuls. Syst. Ser. A"},{"key":"S0218127417502078BIB003","volume-title":"Chaotification of Dynamical Systems: Theory, Methods and Applications","author":"Chen G.","year":"2006"},{"key":"S0218127417502078BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2012.2206936"},{"key":"S0218127417502078BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-1091-5"},{"key":"S0218127417502078BIB006","first-page":"1","volume":"39","author":"Cong N. D.","year":"2016","journal-title":"Electron. J. Qual. Th."},{"key":"S0218127417502078BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.06.008"},{"key":"S0218127417502078BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.09.014"},{"key":"S0218127417502078BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3472-7"},{"key":"S0218127417502078BIB010","unstructured":"Diethelm, K. & Freed, A. D. [1999] The FracPECE Subroutine for the Numerical Solution of Differential Equations of Fractional Order (Gessellschaft fur Wissenschaftliche Datenverarbeitung, Gottingen), pp. 57\u201391."},{"key":"S0218127417502078BIB011","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016592219341"},{"key":"S0218127417502078BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-003-0033-3"},{"key":"S0218127417502078BIB013","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000027736.85078.be"},{"key":"S0218127417502078BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.05.002"},{"key":"S0218127417502078BIB015","doi-asserted-by":"publisher","DOI":"10.1080\/00207160802624331"},{"key":"S0218127417502078BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2013.09.012"},{"key":"S0218127417502078BIB018","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2017-11293-3"},{"key":"S0218127417502078BIB019","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2003.1183"},{"key":"S0218127417502078BIB020","doi-asserted-by":"publisher","DOI":"10.1137\/080718851"},{"key":"S0218127417502078BIB021","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/22\/6\/006"},{"key":"S0218127417502078BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48410-4_7"},{"key":"S0218127417502078BIB023","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.034101"},{"key":"S0218127417502078BIB024","doi-asserted-by":"publisher","DOI":"10.1137\/0906037"},{"key":"S0218127417502078BIB025","volume-title":"Differential Equations, Dynamical Systems and Linear Algebra","author":"Hirsch M. W.","year":"1965"},{"key":"S0218127417502078BIB026","volume-title":"Differential Equations, Dynamical Systems, and An Introduction to Chaos","author":"Hirsch M. W.","year":"2003","edition":"2"},{"key":"S0218127417502078BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2232-9"},{"key":"S0218127417502078BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2011.11.013"},{"key":"S0218127417502078BIB029","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2011-01379-1"},{"key":"S0218127417502078BIB031","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"S0218127417502078BIB033","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717952"},{"key":"S0218127417502078BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-015-0215-9"},{"key":"S0218127417502078BIB035","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18101-6"},{"key":"S0218127417502078BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5767-7"},{"key":"S0218127417502078BIB037","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2007.05.081"},{"key":"S0218127417502078BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.001"},{"key":"S0218127417502078BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.02.023"},{"key":"S0218127417502078BIB040","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/3\/314"},{"key":"S0218127417502078BIB041","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.07.004"},{"key":"S0218127417502078BIB042","doi-asserted-by":"publisher","DOI":"10.1002\/mma.3973"},{"key":"S0218127417502078BIB043","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90011-9"},{"key":"S0218127417502078BIB045","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2011.04.013"},{"key":"S0218127417502078BIB046","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9904-2"},{"key":"S0218127417502078BIB047","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/213485"},{"key":"S0218127417502078BIB048","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.10.008"},{"key":"S0218127417502078BIB049","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.06.030"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417502078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T02:26:07Z","timestamp":1569378367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417502078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,15]]},"references-count":45,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2018,1,3]]},"published-print":{"date-parts":[[2017,12,15]]}},"alternative-id":["10.1142\/S0218127417502078"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417502078","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,15]]}}}