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We give a precise definition for the stable manifold of a saddle slow manifold and design an algorithm to compute it; our computational method is formulated as a two-point boundary value problem that is solved by pseudo-arclength continuation with Auto. We explain how this manifold acts as a separatrix and determines the number of spikes in the transient response generated by a stimulus with fixed amplitude and duration in two different models.<\/jats:p>","DOI":"10.1137\/17m1132458","type":"journal-article","created":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T16:23:04Z","timestamp":1517329384000},"page":"350-379","source":"Crossref","is-referenced-by-count":19,"title":["Computing the Stable Manifold of a Saddle Slow Manifold"],"prefix":"10.1137","volume":"17","author":[{"given":"Saeed","family":"Farjami","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7519-1145","authenticated-orcid":true,"given":"Vivien","family":"Kirk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hinke M.","family":"Osinga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aa675b"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1021\/j100175a053"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1021\/j100041a027"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1186\/2190-8567-2-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1814191"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/070708810"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2009.2.807"},{"key":"atypb8","first-page":"265","volume":"30","author":"Doedel E. 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