{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T18:13:24Z","timestamp":1725646404700},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p> A continuation method (sometimes called path following) is a way to compute solution curves of a nonlinear system of equations with a parameter. We derive a simple algorithm for branch switching at bifurcation points for multiple parameter continuation, where surfaces bifurcate along singular curves on a surface. It is a generalization of the parallel search technique used in the continuation code AUTO, and avoids the need for second derivatives and a full analysis of the bifurcation point. <\/jats:p><jats:p> The one parameter case is special. While the generalization is not difficult, it is nontrivial, and the geometric interpretation may be of some interest. An additional tangent calculation at a point near the singular point is used to estimate the tangent to the singular set. <\/jats:p>","DOI":"10.1142\/s0218127405012375","type":"journal-article","created":{"date-parts":[[2005,5,31]],"date-time":"2005-05-31T12:20:40Z","timestamp":1117542040000},"page":"967-974","source":"Crossref","is-referenced-by-count":10,"title":["MULTIPARAMETER PARALLEL SEARCH BRANCH SWITCHING"],"prefix":"10.1142","volume":"15","author":[{"given":"MICHAEL E.","family":"HENDERSON","sequence":"first","affiliation":[{"name":"IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719154"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01074622"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-575X(02)80025-X"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001576"},{"key":"rf6","volume-title":"Pathways to Solutions, Fixed Points and Equilibria","author":"Garcia C. B.","year":"1981"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719543"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1137\/0150027"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004498"},{"key":"rf10","first-page":"493","volume":"76","author":"Keller H. B.","journal-title":"Math. TODAY"},{"key":"rf11","unstructured":"H. B.\u00a0Keller and E. J.\u00a0Doedel, Sourcebook of Parallel Computing, eds. J.\u00a0Dongarra (Morgan Kaufman, San Francisco, 2003)\u00a0pp. 670\u2013700."},{"key":"rf12","volume-title":"Pattern Formation in Viscous Flows","author":"Meyer-Spasche R.","year":"1991"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01176814"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497001564"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012375","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:06:52Z","timestamp":1565136412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012375"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,3]]}},"alternative-id":["10.1142\/S0218127405012375"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012375","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}