{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T16:11:02Z","timestamp":1784650262166,"version":"3.55.0"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2018istruzione, dell\u2018Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["PRIN 2017LSCR4K"],"award-info":[{"award-number":["PRIN 2017LSCR4K"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> The use of ideal memristors in a continuous-time (CT) nonlinear circuit is known to greatly enrich the dynamic behavior with respect to the memristorless counterpart, which is a crucial property for applications in future analog electronic circuits. This can be explained via the flux\u2013charge analysis method (FCAM), according to which CT circuits with ideal memristors have for structural reasons first integrals (or invariants of motion, or conserved quantities) and their state space can be foliated in infinitely many invariant manifolds where they can display different dynamics. The paper introduces a new discretization scheme for the memristor which, differently from those adopted in the literature, guarantees that the first integrals of the CT memristor circuits are preserved exactly in the discretization, and that this is true for any step size. This new scheme makes it possible to extend FCAM to discrete-time (DT) memristor circuits and rigorously show the existence of invariant manifolds and infinitely many coexisting attractors (extreme multistability). Moreover, the paper addresses standard bifurcations varying the discretization step size and also bifurcations without parameters, i.e. bifurcations due to varying the initial conditions for fixed step size and circuit parameters. The method is illustrated by analyzing the dynamics and flip bifurcations with and without parameters in a DT memristor\u2013capacitor circuit and the Poincar\u00e9\u2013Andronov\u2013Hopf bifurcation in a DT Murali\u2013Lakshmanan\u2013Chua circuit with a memristor. Simulations are also provided to illustrate bifurcations in a higher-order DT memristor Chua\u2019s circuit. The results in the paper show that DT memristor circuits obtained with the proposed discretization scheme are able to display even richer dynamics and bifurcations than their CT counterparts, due to the coexistence of infinitely many attractors and the possibility to use the discretization step as a parameter without destroying the foliation in invariant manifolds. <\/jats:p>","DOI":"10.1142\/s0218127424500019","type":"journal-article","created":{"date-parts":[[2024,2,7]],"date-time":"2024-02-07T10:43:50Z","timestamp":1707302630000},"source":"Crossref","is-referenced-by-count":14,"title":["New Class of Discrete-Time Memristor Circuits: First Integrals, Coexisting Attractors and Bifurcations Without Parameters"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0013-9112","authenticated-orcid":false,"given":"Mauro","family":"Di Marco","sequence":"first","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3970-7201","authenticated-orcid":false,"given":"Mauro","family":"Forti","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2502-9542","authenticated-orcid":false,"given":"Luca","family":"Pancioni","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0234-5999","authenticated-orcid":false,"given":"Alberto","family":"Tesi","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Florence, via Santa Marta 3, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"S0218127424500019BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2021.3133627"},{"key":"S0218127424500019BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/JETCAS.2022.3221156"},{"key":"S0218127424500019BIB003","doi-asserted-by":"publisher","DOI":"10.1049\/el.2016.0563"},{"key":"S0218127424500019BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2021.3082895"},{"key":"S0218127424500019BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112273"},{"key":"S0218127424500019BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300152"},{"key":"S0218127424500019BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741950086X"},{"key":"S0218127424500019BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"S0218127424500019BIB009","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2016.2590948"},{"key":"S0218127424500019BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2016.2642112"},{"key":"S0218127424500019BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-55651-8"},{"key":"S0218127424500019BIB012","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2022.3146419"},{"key":"S0218127424500019BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127423501158"},{"key":"S0218127424500019BIB014","author":"Escudero M.","year":"2023","journal-title":"IEEE Trans. Circuits Syst.-I: Regul. Pap."},{"key":"S0218127424500019BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4426-4"},{"key":"S0218127424500019BIB016","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.035202"},{"key":"S0218127424500019BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2021.3115842"},{"key":"S0218127424500019BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413500983"},{"key":"S0218127424500019BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022354"},{"key":"S0218127424500019BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-02630-5_30"},{"key":"S0218127424500019BIB021","doi-asserted-by":"publisher","DOI":"10.1109\/TETCI.2018.2867375"},{"key":"S0218127424500019BIB022","doi-asserted-by":"publisher","DOI":"10.1038\/nature23307"},{"key":"S0218127424500019BIB023","series-title":"Applied Mathematical Sciences","volume-title":"Elements of Applied Bifurcation Theory","volume":"112","author":"Kuznetsov Y. A.","year":"1998"},{"key":"S0218127424500019BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2020.3022539"},{"key":"S0218127424500019BIB025","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2020.3017286"},{"key":"S0218127424500019BIB026","doi-asserted-by":"publisher","DOI":"10.1063\/1.5042413"},{"key":"S0218127424500019BIB027","doi-asserted-by":"publisher","DOI":"10.1109\/JETCAS.2022.3226900"},{"key":"S0218127424500019BIB028","doi-asserted-by":"publisher","DOI":"10.1002\/cta.2515"},{"key":"S0218127424500019BIB029","doi-asserted-by":"publisher","DOI":"10.1038\/nature06932"},{"key":"S0218127424500019BIB030","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2017.31"},{"key":"S0218127424500019BIB031","doi-asserted-by":"publisher","DOI":"10.1145\/2463585.2463587"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127424500019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,7]],"date-time":"2024-02-07T10:44:18Z","timestamp":1707302658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127424500019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":31,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["10.1142\/S0218127424500019"],"URL":"https:\/\/doi.org\/10.1142\/s0218127424500019","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1]]},"article-number":"2450001"}}