{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T18:40:17Z","timestamp":1775155217662,"version":"3.50.1"},"reference-count":39,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:p>This tutorial investigates bifurcation and chaos in the fractional-order Chen system from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which allows the solution of the fractional differential equations to be written in closed form. By taking advantage of the capabilities given by the decomposition method, the paper illustrates two remarkable findings: (i) chaos exists in the fractional Chen system with order as low as 0.24, which represents the smallest value ever reported in literature for any chaotic system studied so far; (ii) it is feasible to show the occurrence of pitchfork bifurcations and period-doubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.<\/jats:p>","DOI":"10.1142\/s0218127408021415","type":"journal-article","created":{"date-parts":[[2008,9,17]],"date-time":"2008-09-17T11:25:20Z","timestamp":1221650720000},"page":"1845-1863","source":"Crossref","is-referenced-by-count":91,"title":["BIFURCATION AND CHAOS IN THE FRACTIONAL-ORDER CHEN SYSTEM VIA A TIME-DOMAIN APPROACH"],"prefix":"10.1142","volume":"18","author":[{"given":"DONATO","family":"CAFAGNA","sequence":"first","affiliation":[{"name":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GIUSEPPE","family":"GRASSI","sequence":"additional","affiliation":[{"name":"Dipartimento Ingegneria Innovazione, Universit\u00e0 del Salento, Lecce, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.1331"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0895-7177(90)90125-7"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8289-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(96)00171-9"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(02)00438-1"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1093\/ietfec\/e89-a.10.2752"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407017276"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408020550"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1967.tb02303.x"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90222-U"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/9.159595"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"rf13","first-page":"1073","volume":"33","author":"Chua L. O.","journal-title":"IEEE Trans. Circuits Syst.-I"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490220404"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.07.039"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7194"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016592219341"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000027736.85078.be"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.34.4971"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-2664-6_5"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2003.1183"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.09.011"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1109\/81.404062"},{"key":"rf24","volume-title":"Nonlinear Time Series Analysis","author":"Kantz H.","year":"2004"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.035"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.013"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.06.078"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.01.068"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.04.037"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1142\/1997"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.03.014"},{"key":"rf32","volume-title":"The Fractional Calculus","author":"Oldham K. B.","year":"1974"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3486-9"},{"key":"rf34","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00167-9"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1984.1103551"},{"key":"rf37","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1007\/BFb0091924","volume":"98","author":"Takens F.","year":"1981"},{"key":"rf38","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1142\/S0218127400001183","volume":"10","author":"Ueta T.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf39","first-page":"1","volume":"16","author":"Zhang H. B.","journal-title":"Int. J. Mod. Phys. C"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127408021415","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,8]],"date-time":"2020-05-08T09:25:32Z","timestamp":1588929932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127408021415"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":39,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,7]]}},"alternative-id":["10.1142\/S0218127408021415"],"URL":"https:\/\/doi.org\/10.1142\/s0218127408021415","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}