{"id":"https://openalex.org/W2041060868","doi":"https://doi.org/10.1142/s0219525907001227","title":"DOUBLE HOPF BIFURCATION FOR STUART\u2013LANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS","display_name":"DOUBLE HOPF BIFURCATION FOR STUART\u2013LANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W2041060868","doi":"https://doi.org/10.1142/s0219525907001227","mag":"2041060868"},"language":"en","primary_location":{"id":"doi:10.1142/s0219525907001227","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525907001227","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"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":"Advances in Complex Systems","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/A5070448011","display_name":"Suqi Ma","orcid":"https://orcid.org/0000-0001-9267-2389"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"SUQI MA","raw_affiliation_strings":["School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109168411","display_name":"Qishao Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"QISHAO LU","raw_affiliation_strings":["School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013257413","display_name":"S. J. Hogan","orcid":"https://orcid.org/0000-0001-6012-6527"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. JOHN HOGAN","raw_affiliation_strings":["Department of Engineering Mathematics, University of Bristol, BS8 1TR, Bristol, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol, BS8 1TR, Bristol, United Kingdom","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6737,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74090277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"10","issue":"04","first_page":"423","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9997000098228455,"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":0.9997000098228455,"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/T10244","display_name":"Chaos control and synchronization","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8360847234725952},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.6415491104125977},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6061856746673584},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5802008509635925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5636120438575745},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.551727294921875},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5472530722618103},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5249887704849243},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5222247838973999},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5130099654197693},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.5061411261558533},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.48391515016555786},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4533138573169708},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.4416024684906006},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.41484537720680237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36960723996162415},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10253176093101501},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09124535322189331}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8360847234725952},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.6415491104125977},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6061856746673584},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5802008509635925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5636120438575745},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.551727294921875},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5472530722618103},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5249887704849243},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5222247838973999},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5130099654197693},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.5061411261558533},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.48391515016555786},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4533138573169708},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.4416024684906006},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.41484537720680237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36960723996162415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10253176093101501},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09124535322189331},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0219525907001227","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525907001227","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"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":"Advances in Complex Systems","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:10:y:2007:i:04:n:s0219525907001227","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219525907001227","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:10:y:2007:i:04:p:423-448","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0219525907001227","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/06e68466-b649-4c24-a4db-ee82c55882ea","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/06e68466-b649-4c24-a4db-ee82c55882ea","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ma, S, Lu, Q & Hogan, SJ 2007, 'Double Hopf bifurcation for Stuart\u2013Landau system with nonlinear delay feedback and delay-dependent parameters', Advances in Complex Systems, vol. 10, no. 4, pp. 423 - 448. https://doi.org/10.1142/S0219525907001227","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/06e68466-b649-4c24-a4db-ee82c55882ea","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/06e68466-b649-4c24-a4db-ee82c55882ea","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ma, S, Lu, Q & Hogan, SJ 2007, 'Double Hopf bifurcation for Stuart\u2013Landau system with nonlinear delay feedback and delay-dependent parameters', Advances in Complex Systems, vol. 10, no. 4, pp. 423 - 448. https://doi.org/10.1142/S0219525907001227","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1586658033","https://openalex.org/W1963613259","https://openalex.org/W1975781390","https://openalex.org/W1988799042","https://openalex.org/W1999993760","https://openalex.org/W2005488465","https://openalex.org/W2009433941","https://openalex.org/W2010446607","https://openalex.org/W2033270072","https://openalex.org/W2041823824","https://openalex.org/W2054848609","https://openalex.org/W2068386305","https://openalex.org/W2073407203","https://openalex.org/W2088804152","https://openalex.org/W2092007890","https://openalex.org/W2106814660","https://openalex.org/W2114090429","https://openalex.org/W2132434872","https://openalex.org/W2143020650","https://openalex.org/W2152203759","https://openalex.org/W2155289136","https://openalex.org/W2158533181","https://openalex.org/W2158630456","https://openalex.org/W3102439383","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2019027784","https://openalex.org/W2078078632","https://openalex.org/W2347648614","https://openalex.org/W2978098199","https://openalex.org/W2054978396","https://openalex.org/W4293768108","https://openalex.org/W2388294899","https://openalex.org/W2271873789","https://openalex.org/W3015096850"],"abstract_inverted_index":{"A":[0,16],"Stuart\u2013Landau":[1],"system":[2],"under":[3],"delay":[4],"feedback":[5],"control":[6],"with":[7,21],"the":[8,31,89],"nonlinear":[9],"delay-dependent":[10],"parameter":[11],"e":[12],"-p\u03c4":[13],"is":[14,24,71],"investigated.":[15],"geometrical":[17],"demonstration":[18],"method":[19],"combined":[20],"theoretical":[22],"analysis":[23],"developed":[25],"so":[26],"as":[27],"to":[28],"effectively":[29],"solve":[30],"characteristic":[32],"equation.":[33],"Multi-stable":[34],"regions":[35,40],"are":[36,62,82,101,107],"separated":[37],"from":[38],"unstable":[39],"by":[41,58,87],"allocations":[42],"of":[43,95],"Hopf":[44,60,69,79],"bifurcation":[45,61,70,80],"curves":[46],"in":[47,85],"(p,\u03c4)":[48],"plane.":[49],"Some":[50,93],"weak":[51],"resonant":[52],"and":[53,103],"non-resonant":[54],"oscillation":[55],"phenomena":[56],"induced":[57],"double":[59,68,78],"discovered.":[63],"The":[64,73],"normal":[65],"form":[66],"for":[67],"deduced.":[72],"local":[74],"dynamical":[75],"behavior":[76],"near":[77],"points":[81],"also":[83,108],"clarified":[84],"detail":[86],"using":[88],"center":[90],"manifold":[91],"method.":[92],"states":[94],"two":[96],"coexisting":[97],"stable":[98],"periodic":[99],"solutions":[100],"verified,":[102],"some":[104],"torus-broken":[105],"procedures":[106],"traced.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}