{"id":"https://openalex.org/W1986610185","doi":"https://doi.org/10.1142/s0218127401002249","title":"HOMOCLINIC BIFURCATION OF MULTIHARMONIC PERTURBED SYSTEMS","display_name":"HOMOCLINIC BIFURCATION OF MULTIHARMONIC PERTURBED SYSTEMS","publication_year":2001,"publication_date":"2001-02-01","ids":{"openalex":"https://openalex.org/W1986610185","doi":"https://doi.org/10.1142/s0218127401002249","mag":"1986610185"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127401002249","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401002249","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/A5100360124","display_name":"Ke Wang","orcid":"https://orcid.org/0000-0002-6163-4512"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"KE WANG","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086149568","display_name":"Yun Tang","orcid":"https://orcid.org/0000-0001-8709-297X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YUN TANG","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12080448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"02","first_page":"541","last_page":"550"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9991000294685364,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9728422164916992},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.8789113163948059},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7508845329284668},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.634687066078186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5852956175804138},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49831390380859375},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.49563682079315186},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47319647669792175},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.42256560921669006},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.41250449419021606},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32738327980041504},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21462726593017578},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1598922610282898},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14448687434196472},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11875796318054199}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9728422164916992},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.8789113163948059},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7508845329284668},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.634687066078186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5852956175804138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49831390380859375},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.49563682079315186},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47319647669792175},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.42256560921669006},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.41250449419021606},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32738327980041504},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21462726593017578},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1598922610282898},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14448687434196472},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11875796318054199},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127401002249","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401002249","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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1965004685","https://openalex.org/W2039419724","https://openalex.org/W2089876099","https://openalex.org/W2090490710","https://openalex.org/W3123094903"],"related_works":["https://openalex.org/W1999123830","https://openalex.org/W2072009444","https://openalex.org/W3151500797","https://openalex.org/W2350473807","https://openalex.org/W3142626835","https://openalex.org/W2157138821","https://openalex.org/W3145975296","https://openalex.org/W2084618729","https://openalex.org/W3115184012","https://openalex.org/W2085868801"],"abstract_inverted_index":{"The":[0],"dynamics":[1],"of":[2,35,49,60],"homoclinic":[3,26,37,50],"tangencies":[4],"for":[5,52],"a":[6],"multiharmonic":[7],"perturbed":[8],"system":[9],"(MHPS)":[10],"is":[11,45,54],"studied.":[12],"By":[13],"applying":[14],"the":[15,21,25,33,36,47,58],"singularity":[16],"theory":[17],"to":[18,57],"Melnikov":[19],"function":[20],"normal":[22],"forms":[23],"at":[24],"tangency":[27],"points":[28],"are":[29,39],"obtained,":[30],"and":[31],"then":[32],"details":[34],"bifurcation":[38,51],"quite":[40],"clear.":[41],"An":[42],"important":[43],"result":[44],"that":[46],"behavior":[48],"MHPS":[53],"strongly":[55],"related":[56],"number":[59],"harmonic":[61],"components.":[62]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}