{"id":"https://openalex.org/W2069713792","doi":"https://doi.org/10.1137/1017006","title":"Multiple Eigenvalues Lead to Secondary Bifurcation","display_name":"Multiple Eigenvalues Lead to Secondary Bifurcation","publication_year":1975,"publication_date":"1975-01-01","ids":{"openalex":"https://openalex.org/W2069713792","doi":"https://doi.org/10.1137/1017006","mag":"2069713792"},"language":"en","primary_location":{"id":"doi:10.1137/1017006","doi":"https://doi.org/10.1137/1017006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1017006","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Louis Bauer","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Louis Bauer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006401781","display_name":"Herbert B. Keller","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Herbert B. Keller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111845582","display_name":"Edward L. Reiss","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edward L. Reiss","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.0506,"has_fulltext":false,"cited_by_count":178,"citation_normalized_percentile":{"value":0.96895307,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"101","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7939000129699707,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.7939000129699707,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.07989999651908875,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.0406000018119812,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/secondary-bifurcation","display_name":"secondary bifurcation","score":0.8970000147819519},{"id":"https://openalex.org/keywords/multiple-eigenvalues","display_name":"multiple eigenvalues","score":0.8939999938011169},{"id":"https://openalex.org/keywords/bifurcation-points","display_name":"bifurcation points","score":0.7789999842643738},{"id":"https://openalex.org/keywords/two-degree-of-freedom-system","display_name":"two-degree-of-freedom system","score":0.875},{"id":"https://openalex.org/keywords/plate-buckling","display_name":"plate buckling","score":0.8899999856948853},{"id":"https://openalex.org/keywords/rod-buckling","display_name":"rod buckling","score":0.996999979019165},{"id":"https://openalex.org/keywords/axisymmetric-buckling","display_name":"axisymmetric buckling","score":0.8460000157356262},{"id":"https://openalex.org/keywords/spherical-shell","display_name":"spherical shell","score":0.9580000042915344},{"id":"https://openalex.org/keywords/perturbation-method","display_name":"perturbation method","score":0.8029999732971191},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.3779999911785126}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.868432879447937},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7272473573684692},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.7249220013618469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5738430619239807},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5710320472717285},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5546855330467224},{"id":"https://openalex.org/C85476182","wikidata":"https://www.wikidata.org/wiki/Q693104","display_name":"Buckling","level":2,"score":0.5466610789299011},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.5112993717193604},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.501502275466919},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.49508920311927795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4548145532608032},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.4304535984992981},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41557803750038147},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.328644335269928},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31570199131965637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20457828044891357},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08290570974349976},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06115105748176575},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1017006","doi":"https://doi.org/10.1137/1017006","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1017006","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W159546068","https://openalex.org/W323901367","https://openalex.org/W1612422762","https://openalex.org/W1981985387","https://openalex.org/W1982525673","https://openalex.org/W1985282494","https://openalex.org/W2004282094","https://openalex.org/W2017267758","https://openalex.org/W2024882614","https://openalex.org/W2026177062","https://openalex.org/W2036536795","https://openalex.org/W2088509655","https://openalex.org/W2106988076","https://openalex.org/W2119213531","https://openalex.org/W2149217060","https://openalex.org/W2525196761","https://openalex.org/W2565460196","https://openalex.org/W4297672074","https://openalex.org/W4297932197"],"related_works":["https://openalex.org/W2043617693","https://openalex.org/W2094963618","https://openalex.org/W2084755692","https://openalex.org/W152068251","https://openalex.org/W2009772047","https://openalex.org/W3042324601","https://openalex.org/W2002115361","https://openalex.org/W2735760425","https://openalex.org/W1978472514","https://openalex.org/W2477121900"],"abstract_inverted_index":{"Bifurcation":[0],"problems":[1,112,143],"are":[2,9],"considered":[3],"where":[4,144,151],"the":[5,64,94,127,152],"primary":[6,39,65],"bifurcation":[7,22,40,45],"points":[8,41,46,57],"functions":[10],"of":[11,63,130,140],"a":[12,20,77,83,137],"parameter":[13],"$\\tau":[14,27,48,52,68],"$.":[15,54],"It":[16],"is":[17,72,82,108,120],"shown":[18,73],"that":[19,93],"multiple":[21],"point,":[23],"which":[24,81,113],"occurs":[25,96],"for":[26,76,85,110],"=":[28],"\\tau":[29],"_0":[30,53],"$,":[31],"may":[32,148,155],"\u201csplit\u201d":[33],"into":[34],"two":[35],"(or":[36],"more)":[37],"simple":[38,78],"and":[42,87,100,150],"several":[43,98],"secondary":[44,56,124],"as":[47,67],"$":[49,69],"varies":[50],"from":[51],"These":[55],"move":[58],"along":[59],"one":[60],"or":[61],"more":[62],"branches":[66],"varies.":[70],"This":[71,90],"to":[74,122],"occur":[75,149],"two-degrees-of-freedom":[79],"system,":[80],"model":[84],"plate":[86],"rod":[88],"buckling.":[89],"analysis":[91],"shows":[92],"splitting":[95],"in":[97,126],"different":[99],"physically":[101],"significant":[102],"ways.":[103],"A":[104],"new":[105,146],"perturbation":[106,153],"method":[107,119,154],"presented":[109],"analyzing":[111],"cannot":[114],"be":[115,156],"explicitly":[116],"solved.":[117],"The":[118,133],"applied":[121],"study":[123],"bifurcations":[125],"axisymmetric":[128],"buckling":[129],"spherical":[131],"shells.":[132],"paper":[134],"concludes":[135],"with":[136],"brief":[138],"discussion":[139],"some":[141],"physical":[142],"this":[145],"phenomenon":[147],"applicable.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
