{"id":"https://openalex.org/W1973416719","doi":"https://doi.org/10.1142/s0218127409024542","title":"BIFURCATION ANALYSIS OF THE SWIFT\u2013HOHENBERG EQUATION WITH QUINTIC NONLINEARITY","display_name":"BIFURCATION ANALYSIS OF THE SWIFT\u2013HOHENBERG EQUATION WITH QUINTIC NONLINEARITY","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W1973416719","doi":"https://doi.org/10.1142/s0218127409024542","mag":"1973416719"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409024542","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024542","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"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":"https://openalex.org/A5035507977","display_name":"Qingkun Xiao","orcid":"https://orcid.org/0000-0002-6341-8792"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"QINGKUN XIAO","raw_affiliation_strings":["Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042141840","display_name":"Hui Gao","orcid":"https://orcid.org/0000-0002-5111-1179"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"HONGJUN GAO","raw_affiliation_strings":["Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China","institution_ids":["https://openalex.org/I152031979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035507977"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"apc_list":null,"apc_paid":null,"fwci":0.6857,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.70529077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"09","first_page":"2927","last_page":"2937"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.797839343547821},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6963921785354614},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.692581057548523},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6922727227210999},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6625847816467285},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5956161618232727},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5620295405387878},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5607537627220154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.544540524482727},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5161646008491516},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5140248537063599},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5082911849021912},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.49710872769355774},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.48654428124427795},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20012381672859192},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.08204910159111023}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.797839343547821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6963921785354614},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.692581057548523},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6922727227210999},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6625847816467285},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5956161618232727},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5620295405387878},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5607537627220154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.544540524482727},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5161646008491516},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5140248537063599},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5082911849021912},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.49710872769355774},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.48654428124427795},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20012381672859192},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.08204910159111023},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409024542","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024542","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1557040331","https://openalex.org/W2000883601","https://openalex.org/W2001675348","https://openalex.org/W2004785198","https://openalex.org/W2007794758","https://openalex.org/W2032883337","https://openalex.org/W2043991004","https://openalex.org/W2044106245","https://openalex.org/W2049937590","https://openalex.org/W2061883026","https://openalex.org/W2068037089","https://openalex.org/W2075645817","https://openalex.org/W2082786393"],"related_works":["https://openalex.org/W2057674154","https://openalex.org/W1976081455","https://openalex.org/W2025138898","https://openalex.org/W2078078632","https://openalex.org/W1927500429","https://openalex.org/W2923981205","https://openalex.org/W2021742636","https://openalex.org/W4249362477","https://openalex.org/W2347648614","https://openalex.org/W3023422590"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,73],"concerned":[3],"with":[4,16,76],"the":[5,9,13,28,32,44,63,70,77,89,95],"asymptotic":[6],"behavior":[7,53],"of":[8,12,31,39,54,79,86],"solutions":[10,41,64],"u(x,t)":[11,65],"Swift\u2013Hohenberg":[14],"equation":[15],"quintic":[17],"nonlinearity":[18],"on":[19],"a":[20,80],"one-dimensional":[21],"domain":[22,33],"(0,":[23],"L).":[24],"With":[25],"\u03b1":[26],"and":[27,68,100],"length":[29],"L":[30],"regarded":[34],"as":[35],"bifurcation":[36,90,96],"parameters,":[37],"branches":[38,56],"nontrivial":[40],"bifurcating":[42],"from":[43],"trivial":[45],"solution":[46],"at":[47],"certain":[48],"points":[49,97],"are":[50,57,66,92,98,103],"shown.":[51],"Local":[52],"these":[55],"also":[58],"studied.":[59],"Global":[60],"bounds":[61],"for":[62],"established":[67],"then":[69],"global":[71],"attractor":[72],"investigated.":[74],"Finally,":[75],"help":[78],"center":[81],"manifold":[82],"analysis,":[83],"two":[84],"types":[85],"structures":[87],"in":[88],"diagrams":[91],"presented":[93],"when":[94],"closer,":[99],"their":[101],"stabilities":[102],"analyzed.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}