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The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties. <\/jats:p>","DOI":"10.1142\/s0218127416500644","type":"journal-article","created":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T04:18:02Z","timestamp":1462421882000},"page":"1650064","source":"Crossref","is-referenced-by-count":1,"title":["Saddle-Node Bifurcations in Classical and Memristive Circuits"],"prefix":"10.1142","volume":"26","author":[{"given":"Ignacio","family":"Garc\u00eda de la Vega","sequence":"first","affiliation":[{"name":"Depto.\u00a0de Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n y las Comunicaciones, Escuela T\u00e9cnica Superior de Ingenieros de Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s\/n \u2013 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Riaza","sequence":"additional","affiliation":[{"name":"Depto.\u00a0de Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n y las Comunicaciones, Escuela T\u00e9cnica Superior de Ingenieros de Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s\/n \u2013 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,5,5]]},"reference":[{"key":"S0218127416500644BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-02630-5"},{"key":"S0218127416500644BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719154"},{"key":"S0218127416500644BIB003","volume-title":"Graph Theory: Flows, Matrices","author":"Andr\u00e1sfai B.","year":"1991"},{"key":"S0218127416500644BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989936457X"},{"key":"S0218127416500644BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0619-4"},{"key":"S0218127416500644BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/169747"},{"key":"S0218127416500644BIB007","volume-title":"Numerical Solution of Initial-Value Problems in Differential Algebraic Equations","author":"Brenan K. 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