{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T21:13:54Z","timestamp":1770153234529,"version":"3.49.0"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60873200"],"award-info":[{"award-number":["60873200"]}],"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":[[2016,3]]},"abstract":"<jats:p> In this paper, chaos in complex-order Chua\u2019s system and its chaotic synchronization for secure communication are studied based on the fractional derivative investigated. Chaos in complex-order Chua\u2019s system is illustrated by presenting its waveform graphs, states diagrams and bifurcation graphs. The dynamic behaviors in the complex-order Chua\u2019s system and time-delayed Chua\u2019s system are compared. In addition, the largest Lyapunov exponents of normal and time-delayed Chua\u2019s systems are calculated and verified by numerical simulations. The experiment indicates that the chaos in such Chua\u2019s system can achieve two channel communications. <\/jats:p>","DOI":"10.1142\/s0218127416500462","type":"journal-article","created":{"date-parts":[[2016,4,5]],"date-time":"2016-04-05T23:23:16Z","timestamp":1459898596000},"page":"1650046","source":"Crossref","is-referenced-by-count":17,"title":["Chaos and Synchronization in Complex Fractional-Order Chua\u2019s System"],"prefix":"10.1142","volume":"26","author":[{"given":"Xiaoran","family":"Lin","sequence":"first","affiliation":[{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Department of Computer Science, Chongqing University, Chongqing 400044, P. R. China"}]},{"given":"Shangbo","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Department of Computer Science, Chongqing University, Chongqing 400044, P. R. China"}]},{"given":"Hua","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Lethbridge, Canada"}]}],"member":"219","published-online":{"date-parts":[[2016,4,5]]},"reference":[{"key":"S0218127416500462BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90994-B"},{"key":"S0218127416500462BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(00)00352-9"},{"key":"S0218127416500462BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2006.01.006"},{"key":"S0218127416500462BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/9789812817747_0001"},{"key":"S0218127416500462BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2006.06.010"},{"key":"S0218127416500462BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.01.021"},{"key":"S0218127416500462BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2008.10.009"},{"key":"S0218127416500462BIB008","doi-asserted-by":"publisher","DOI":"10.1063\/1.166330"},{"key":"S0218127416500462BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0983-6"},{"key":"S0218127416500462BIB010","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Kenneth S. M.","year":"1993"},{"key":"S0218127416500462BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00240-1"},{"key":"S0218127416500462BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.06.078"},{"key":"S0218127416500462BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005819"},{"key":"S0218127416500462BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015179"},{"key":"S0218127416500462BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-008-9343-5"},{"key":"S0218127416500462BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9637-2"},{"key":"S0218127416500462BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2010.03.012"},{"key":"S0218127416500462BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029859"},{"key":"S0218127416500462BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029525"},{"key":"S0218127416500462BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0091-6"},{"key":"S0218127416500462BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0937-1"},{"key":"S0218127416500462BIB022","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/87\/05\/055002"},{"key":"S0218127416500462BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1984.1085459"},{"key":"S0218127416500462BIB024","doi-asserted-by":"publisher","DOI":"10.1063\/1.165851"},{"key":"S0218127416500462BIB025","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.821"},{"key":"S0218127416500462BIB026","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412500642"},{"key":"S0218127416500462BIB027","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415500030"},{"key":"S0218127416500462BIB028","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"},{"key":"S0218127416500462BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90009-P"},{"key":"S0218127416500462BIB030","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"Samko S. G.","year":"1993"},{"key":"S0218127416500462BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.04.029"},{"key":"S0218127416500462BIB032","doi-asserted-by":"publisher","DOI":"10.1142\/S0217979210057596"},{"key":"S0218127416500462BIB033","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.03.021"},{"key":"S0218127416500462BIB034","doi-asserted-by":"publisher","DOI":"10.1063\/1.2755420"},{"key":"S0218127416500462BIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0217979211058638"},{"key":"S0218127416500462BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2008.05.002"},{"key":"S0218127416500462BIB037","first-page":"803","volume":"11","author":"Wang Y.","year":"2010","journal-title":"Int. J. Nonlin. Sci."},{"key":"S0218127416500462BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2012.01.002"},{"key":"S0218127416500462BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90011-9"},{"key":"S0218127416500462BIB040","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(01)00157-1"},{"key":"S0218127416500462BIB041","first-page":"55","volume":"146","author":"Youngman A.","year":"1995","journal-title":"New Scientist"},{"key":"S0218127416500462BIB043","first-page":"157","volume":"11","author":"Zhang Y.","year":"2010","journal-title":"Int. J. Nonlin. Sci."},{"key":"S0218127416500462BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.06.082"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416500462","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T00:40:10Z","timestamp":1569285610000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416500462"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":43,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2016,4,5]]},"published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.1142\/S0218127416500462"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416500462","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}