{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:46:44Z","timestamp":1760784404734,"version":"3.37.3"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51507134"],"award-info":[{"award-number":["51507134"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,15]]},"abstract":"<jats:p> Memristor is a nonlinear \u201cmissing circuit element\u201d, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua\u2019s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation. <\/jats:p>","DOI":"10.1142\/s0218127417501991","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T03:03:43Z","timestamp":1514948623000},"page":"1750199","source":"Crossref","is-referenced-by-count":29,"title":["Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7219-484X","authenticated-orcid":false,"given":"Ningning","family":"yang","sequence":"first","affiliation":[{"name":"State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi\u2019an University of Technology, Xi\u2019an, P. R. China"},{"name":"Institute of Water Resources and Hydro-Electric Engineering, Xi\u2019an University of Technology, Xi\u2019an, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Water Resources and Hydro-Electric Engineering, Xi\u2019an University of Technology, Xi\u2019an, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3644-4354","authenticated-orcid":false,"given":"Chaojun","family":"wu","sequence":"additional","affiliation":[{"name":"College of Electronics and Information, Xi\u2019an Polytechnic University, Xi\u2019an, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3497-6506","authenticated-orcid":false,"given":"Rong","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi\u2019an University of Technology, Xi\u2019an, P. R. China"},{"name":"Institute of Water Resources and Hydro-Electric Engineering, Xi\u2019an University of Technology, Xi\u2019an, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8427-0937","authenticated-orcid":false,"given":"Chongxin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,1,3]]},"reference":[{"key":"S0218127417501991BIB001","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/19\/3\/030510"},{"key":"S0218127417501991BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501430"},{"key":"S0218127417501991BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0522-z"},{"key":"S0218127417501991BIB004","doi-asserted-by":"publisher","DOI":"10.3390\/e16126464"},{"key":"S0218127417501991BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s12043-014-0880-9"},{"key":"S0218127417501991BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"S0218127417501991BIB007","doi-asserted-by":"publisher","DOI":"10.1049\/el.2012.1480"},{"key":"S0218127417501991BIB008","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016592219341"},{"key":"S0218127417501991BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00339-011-6318-z"},{"key":"S0218127417501991BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2011.2136443"},{"key":"S0218127417501991BIB011","first-page":"1","volume":"4","author":"Fouda M. E.","year":"2013","journal-title":"J. Fract. Calculus Appl."},{"key":"S0218127417501991BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.10.028"},{"key":"S0218127417501991BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022354"},{"key":"S0218127417501991BIB018","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0553"},{"key":"S0218127417501991BIB019","doi-asserted-by":"publisher","DOI":"10.1063\/1.4934653"},{"key":"S0218127417501991BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-015-0024-5"},{"key":"S0218127417501991BIB021","doi-asserted-by":"publisher","DOI":"10.1109\/LED.2013.2284927"},{"key":"S0218127417501991BIB022","doi-asserted-by":"publisher","DOI":"10.4103\/0256-4602.57827"},{"key":"S0218127417501991BIB023","first-page":"396","volume":"56","author":"Oldham K. B.","year":"1974","journal-title":"Math. Gaz."},{"key":"S0218127417501991BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/81.817385"},{"key":"S0218127417501991BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1882-3"},{"key":"S0218127417501991BIB027","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2010.2083150"},{"key":"S0218127417501991BIB028","doi-asserted-by":"crossref","first-page":"205","DOI":"10.25103\/jestr.082.26","volume":"8","author":"Pham V. T.","year":"2015","journal-title":"J. Engin. Sci. Technol. Rev."},{"volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications","year":"1998","author":"Podlubny I.","key":"S0218127417501991BIB029"},{"key":"S0218127417501991BIB030","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2014.2312806"},{"key":"S0218127417501991BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.mejo.2016.02.005"},{"key":"S0218127417501991BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3215-1"},{"key":"S0218127417501991BIB033","doi-asserted-by":"publisher","DOI":"10.1038\/nature06932"},{"key":"S0218127417501991BIB034","doi-asserted-by":"publisher","DOI":"10.3103\/S1060992X15020125"},{"key":"S0218127417501991BIB035","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/22\/3\/030506"},{"key":"S0218127417501991BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/s10470-016-0795-0"},{"key":"S0218127417501991BIB037","first-page":"1","volume":"6","author":"Wu C.","year":"2015","journal-title":"Math. Probl. Engin."},{"key":"S0218127417501991BIB038","first-page":"22","volume":"27","author":"Zhong Q. S.","year":"2010","journal-title":"Chinese Phys. Lett."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417501991","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:01:58Z","timestamp":1565078518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417501991"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,15]]},"references-count":33,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2018,1,3]]},"published-print":{"date-parts":[[2017,12,15]]}},"alternative-id":["10.1142\/S0218127417501991"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417501991","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,12,15]]}}}