{"id":"https://openalex.org/W2139019963","doi":"https://doi.org/10.1007/s11075-010-9404-y","title":"Analytical approximations for the periodic motion of the Duffing system with delayed feedback","display_name":"Analytical approximations for the periodic motion of the Duffing system with delayed feedback","publication_year":2010,"publication_date":"2010-06-22","ids":{"openalex":"https://openalex.org/W2139019963","doi":"https://doi.org/10.1007/s11075-010-9404-y","mag":"2139019963"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-010-9404-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-010-9404-y","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5103174191","display_name":"Xiangcheng You","orcid":"https://orcid.org/0000-0003-4954-9152"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I44675526","display_name":"Shanghai Ocean University","ror":"https://ror.org/04n40zv07","country_code":"CN","type":"education","lineage":["https://openalex.org/I44675526"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangcheng You","raw_affiliation_strings":["State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China","institution_ids":["https://openalex.org/I44675526","https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066768790","display_name":"Hang Xu","orcid":"https://orcid.org/0000-0003-4176-0738"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I44675526","display_name":"Shanghai Ocean University","ror":"https://ror.org/04n40zv07","country_code":"CN","type":"education","lineage":["https://openalex.org/I44675526"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hang Xu","raw_affiliation_strings":["State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China","institution_ids":["https://openalex.org/I44675526","https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103174191"],"corresponding_institution_ids":["https://openalex.org/I183067930","https://openalex.org/I44675526"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.9443,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.75784979,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"4","first_page":"561","last_page":"576"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9921000003814697,"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/T10244","display_name":"Chaos control and synchronization","score":0.9818999767303467,"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/mathematics","display_name":"Mathematics","score":0.7613682150840759},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6975539922714233},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.5799434185028076},{"id":"https://openalex.org/keywords/duffing-equation","display_name":"Duffing equation","score":0.5598019361495972},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5499937534332275},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.536300539970398},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5193504095077515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.485696405172348},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4552738070487976},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43052583932876587},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40080526471138},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3875438868999481},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2936133146286011},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10573956370353699},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08830085396766663},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08308082818984985}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7613682150840759},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6975539922714233},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.5799434185028076},{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.5598019361495972},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5499937534332275},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.536300539970398},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5193504095077515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.485696405172348},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4552738070487976},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43052583932876587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40080526471138},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3875438868999481},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2936133146286011},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10573956370353699},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08830085396766663},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08308082818984985},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-010-9404-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-010-9404-y","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8799999952316284,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W200840997","https://openalex.org/W1487864787","https://openalex.org/W1586658033","https://openalex.org/W1964997874","https://openalex.org/W1973000709","https://openalex.org/W1976196891","https://openalex.org/W1976367203","https://openalex.org/W1977344101","https://openalex.org/W1981944861","https://openalex.org/W1983171862","https://openalex.org/W1988797736","https://openalex.org/W1998901158","https://openalex.org/W2007456116","https://openalex.org/W2011676446","https://openalex.org/W2015727116","https://openalex.org/W2019311512","https://openalex.org/W2021387863","https://openalex.org/W2026498908","https://openalex.org/W2035719659","https://openalex.org/W2038197536","https://openalex.org/W2038454880","https://openalex.org/W2042677872","https://openalex.org/W2044477139","https://openalex.org/W2049273606","https://openalex.org/W2057323358","https://openalex.org/W2059348829","https://openalex.org/W2060813275","https://openalex.org/W2062341116","https://openalex.org/W2063222758","https://openalex.org/W2068386305","https://openalex.org/W2068551947","https://openalex.org/W2070999752","https://openalex.org/W2076337319","https://openalex.org/W2082305832","https://openalex.org/W2088804152","https://openalex.org/W2090569656","https://openalex.org/W2119794696","https://openalex.org/W2134086237","https://openalex.org/W2143042816","https://openalex.org/W2144522870","https://openalex.org/W2155289136","https://openalex.org/W2168825792","https://openalex.org/W2276383495","https://openalex.org/W2353306489","https://openalex.org/W2376026223","https://openalex.org/W2391791222","https://openalex.org/W2566180407","https://openalex.org/W3102439383","https://openalex.org/W4254879547"],"related_works":["https://openalex.org/W2391752819","https://openalex.org/W2015757695","https://openalex.org/W1976870670","https://openalex.org/W2090825619","https://openalex.org/W2374687872","https://openalex.org/W2362256999","https://openalex.org/W2800520120","https://openalex.org/W2007245702","https://openalex.org/W2921340142","https://openalex.org/W2048873866"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
