{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T18:02:00Z","timestamp":1787508120811,"version":"build-2736575974"},"reference-count":51,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:p>The recent discovery of a physical device behaving as a memristor has driven a lot of attention to memristive systems, which are likely to play a relevant role in electronics in the near future, especially at the nanometer scale. The derivation of explicit ODE models for these systems is important because it opens a way for the study of the dynamics of general memristive circuits, including e.g. stability aspects, oscillations, bifurcations or chaotic phenomena. We tackle this problem as a reduction of implicit ODE (differential-algebraic) models, and show how tree-based approaches can be adapted in order to accommodate memristors. Specifically, we prove that the derivation of a tree-based explicit ODE model is feasible for strictly passive memristive systems under broad coupling effects and without a priori current\/voltage control assumptions on tree\/cotree elements. Our framework applies in particular to topologically degenerate circuits and accommodates a wide class of controlled sources. We also discuss a quasilinear reduction of nonpassive problems, which do not admit an explicit ODE description in the presence of singularities; some related bifurcations are addressed in this context.<\/jats:p>","DOI":"10.1142\/s0218127411028714","type":"journal-article","created":{"date-parts":[[2011,4,11]],"date-time":"2011-04-11T21:12:58Z","timestamp":1302556378000},"page":"917-930","source":"Crossref","is-referenced-by-count":9,"title":["EXPLICIT ODE REDUCTION OF MEMRISTIVE SYSTEMS"],"prefix":"10.1142","volume":"21","author":[{"given":"RICARDO","family":"RIAZA","sequence":"first","affiliation":[{"name":"Departamento Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n, ETSI Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1957.1086361"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989936457X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1049\/el.2009.3511"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0619-4"},{"key":"rf5","volume-title":"Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations","author":"Brenan K. 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