{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:36:08Z","timestamp":1787236568940,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["643073"],"award-info":[{"award-number":["643073"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["754462"],"award-info":[{"award-number":["754462"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["RTI2018-096523-B-I00"],"award-info":[{"award-number":["RTI2018-096523-B-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\\,x+p(t)$, where $q\\colon\\mathbb R\\to\\mathbb R$ and $p\\colon\\mathbb R\\to\\mathbb R$ are bounded and uniformly continuous, is fundamental to explaining the absence or occurrence of rate-induced tipping for the differential equation $y' =(y-(2\/\\pi)\\arctan(ct))^2+p(t)$ as the rate $c$ varies on $[0,\\infty)$. A classical attractor-repeller pair, whose existence for $c=0$ is assumed, may persist for any $c&gt;0$, or disappear for a certain critical rate $c=c_0$, giving rise to rate-induced tipping. A suitable example demonstrates that one can have more than one critical rate, and the existence of the classical attractor-repeller pair may return when $c$ increases.<\/jats:p>","DOI":"10.1137\/20m1339003","type":"journal-article","created":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T09:57:22Z","timestamp":1616061442000},"page":"500-540","source":"Crossref","is-referenced-by-count":24,"title":["Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics"],"prefix":"10.1137","volume":"20","author":[{"given":"Iacopo P.","family":"Longo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carmen","family":"N\u00fan\u0342ez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rafael","family":"Obaya","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Rasmussen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,3,18]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5000418"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2019.0051"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500002389"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-02-06692-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.03.016"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aa675b"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2011.0306"},{"key":"atypb8","unstructured":"G. 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