{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:26:32Z","timestamp":1787239592927,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We describe a new variant of the so-called homoclinic snaking mechanism for the generation of infinitely many distinct localized patterns in spatially reversible partial differential equations on the real line. In standard snaking a branch of localized states undergoes infinitely many folds as the pattern grows in length by adding cells at either side. In the cases studied here the localized states have a defect or hump in the middle corresponding to an additional orbit homoclinic to the underlying spatially periodic orbit, and the folds accumulate on a parameter value where the periodic orbit undergoes a saddle-center transition. By analyzing an appropriate normal form in a spatial dynamics approach, it is shown that convergence of the folds is algebraic rather than exponential. Specifically the parameter value of the $n$th fold scales like $n^{-4}$. The transition from this saddle-center mediated snaking to regular snaking is described by a codimension-two bifurcation that is also analyzed. The results are compared with numerical computations on two distinct complex Ginzburg--Landau models, one of which is variational and so represents a conservative system in space, while the other is nonvariational. Good agreement with the theory is found in both cases, and the connection between the theory and the recently identified defect-mediated snaking is established.<\/jats:p>","DOI":"10.1137\/110855429","type":"journal-article","created":{"date-parts":[[2012,11,27]],"date-time":"2012-11-27T10:18:02Z","timestamp":1354011482000},"page":"1583-1613","source":"Crossref","is-referenced-by-count":12,"title":["Homoclinic Snakes Bounded by a Saddle-Center Periodic Orbit"],"prefix":"10.1137","volume":"11","author":[{"given":"A. R.","family":"Champneys","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Knobloch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Y.-P.","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Wagenknecht","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,11,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/100782747"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/080713306"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.046201"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.036214"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.036202"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.73.056211"},{"key":"atypb7","unstructured":"J. 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