{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T18:40:08Z","timestamp":1775155208501,"version":"3.50.1"},"reference-count":70,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,9]]},"abstract":"<jats:p> This paper deals with fractional order Chua system with cubic nonlinearity (cubic Chua system), which is a modification of Chua system. The aim is, first, to study the chaotic behavior in fractional order cubic Chua system. We found that chaos indeed exists in the fractional version of this system. The necessary condition for exhibiting chaotic attractors similar to its integer order counterpart is presented. This condition is used to distinguish for which parameters and orders the system generates double scroll chaotic attractors. The synchronization problem between two coupled chaotic fractional order cubic Chua systems is then addressed. An adaptive feedback control scheme for the synchronization with suitable feedback nonlinear controller applied to the response system is presented. Numerical simulations are performed to verify the theoretical analysis. <\/jats:p>","DOI":"10.1142\/s0218127417501619","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T23:03:49Z","timestamp":1507849429000},"page":"1750161","source":"Crossref","is-referenced-by-count":38,"title":["Chaos in Fractional Order Cubic Chua System and Synchronization"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2414-7969","authenticated-orcid":false,"given":"Zaid","family":"Odibat","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Nathalie","family":"Corson","sequence":"additional","affiliation":[{"name":"Appl. Math. Lab., University of Le Havre, 76058, Le Havre Cedex, France"}]},{"given":"M. A.","family":"Aziz-Alaoui","sequence":"additional","affiliation":[{"name":"Appl. Math. Lab., University of Le Havre, 76058, Le Havre Cedex, France"}]},{"given":"Ahmed","family":"Alsaedi","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]}],"member":"219","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"S0218127417501619BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.01.087"},{"key":"S0218127417501619BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90093-4"},{"key":"S0218127417501619BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/B0-12-512666-2\/00105-X"},{"key":"S0218127417501619BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.01.004"},{"key":"S0218127417501619BIB005","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1967.tb02303.x"},{"key":"S0218127417501619BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2017.07.004"},{"key":"S0218127417501619BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/b79666"},{"key":"S0218127417501619BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1986.1085869"},{"key":"S0218127417501619BIB009","doi-asserted-by":"publisher","DOI":"10.1109\/31.55064"},{"key":"S0218127417501619BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126693000071"},{"key":"S0218127417501619BIB011","first-page":"89","volume":"257","author":"Danca M.-F.","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"S0218127417501619BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.01.021"},{"key":"S0218127417501619BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-006-9094-0"},{"key":"S0218127417501619BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.10.010"},{"key":"S0218127417501619BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.11.059"},{"key":"S0218127417501619BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-2664-6_5"},{"key":"S0218127417501619BIB017","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.034101"},{"key":"S0218127417501619BIB019","doi-asserted-by":"publisher","DOI":"10.1109\/81.404062"},{"key":"S0218127417501619BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.09.026"},{"key":"S0218127417501619BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/3779"},{"key":"S0218127417501619BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2016.10.123"},{"key":"S0218127417501619BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496001454"},{"key":"S0218127417501619BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(95)00276-6"},{"key":"S0218127417501619BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.11.007"},{"key":"S0218127417501619BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2004.04.113"},{"key":"S0218127417501619BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.035"},{"key":"S0218127417501619BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.09.012"},{"key":"S0218127417501619BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.06.078"},{"key":"S0218127417501619BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.11.020"},{"key":"S0218127417501619BIB031","author":"Li M.","year":"2010","journal-title":"Math. Probl. Engin."},{"key":"S0218127417501619BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0210-4"},{"key":"S0218127417501619BIB033","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.04.037"},{"key":"S0218127417501619BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0495-y"},{"key":"S0218127417501619BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.01.005"},{"key":"S0218127417501619BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9609-6"},{"key":"S0218127417501619BIB038","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410025429"},{"key":"S0218127417501619BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2011.08.016"},{"key":"S0218127417501619BIB040","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"S0218127417501619BIB041","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.12.007"},{"key":"S0218127417501619BIB042","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.821"},{"key":"S0218127417501619BIB043","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.11.053"},{"key":"S0218127417501619BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.10.054"},{"key":"S0218127417501619BIB045","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"},{"key":"S0218127417501619BIB046","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"Samko S. G.","year":"1993"},{"key":"S0218127417501619BIB047","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.07.009"},{"key":"S0218127417501619BIB048","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.11.018"},{"key":"S0218127417501619BIB049","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.073"},{"key":"S0218127417501619BIB050","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2011.12.006"},{"key":"S0218127417501619BIB051","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2017.01.017"},{"key":"S0218127417501619BIB052","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.02.015"},{"key":"S0218127417501619BIB053","volume-title":"Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media","author":"Tarasov V.","year":"2011"},{"key":"S0218127417501619BIB054","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2007.05.081"},{"key":"S0218127417501619BIB055","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2008.07.003"},{"key":"S0218127417501619BIB056","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.02.023"},{"key":"S0218127417501619BIB057","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.03.021"},{"key":"S0218127417501619BIB058","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0322-x"},{"key":"S0218127417501619BIB059","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.06.145"},{"key":"S0218127417501619BIB060","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.05.045"},{"key":"S0218127417501619BIB061","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(02)00360-3"},{"key":"S0218127417501619BIB062","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-008-9416-5"},{"key":"S0218127417501619BIB063","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9658-x"},{"key":"S0218127417501619BIB064","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.70.1240"},{"key":"S0218127417501619BIB065","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.11.062"},{"key":"S0218127417501619BIB066","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.10.061"},{"key":"S0218127417501619BIB067","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00318-6"},{"key":"S0218127417501619BIB068","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.04.005"},{"key":"S0218127417501619BIB069","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9904-2"},{"key":"S0218127417501619BIB070","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-9944-2"},{"key":"S0218127417501619BIB071","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.07.033"},{"key":"S0218127417501619BIB072","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\/S0218127417501619","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:11:54Z","timestamp":1565183514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417501619"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9]]},"references-count":70,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10,12]]},"published-print":{"date-parts":[[2017,9]]}},"alternative-id":["10.1142\/S0218127417501619"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417501619","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9]]}}}