{"id":"https://openalex.org/W3134832663","doi":"https://doi.org/10.1137/20m1325101","title":"High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities","display_name":"High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3134832663","doi":"https://doi.org/10.1137/20m1325101","mag":"3134832663"},"language":"en","primary_location":{"id":"doi:10.1137/20m1325101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1325101","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://scholars.cityu.edu.hk/en/publications/high-order-approximation-of-heteroclinic-bifurcations-in-truncate","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081761194","display_name":"Bo-Wei Qin","orcid":"https://orcid.org/0000-0002-0745-0755"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. W. Qin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024341642","display_name":"K.W. Chung","orcid":"https://orcid.org/0000-0002-0153-8801"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. W. Chung","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0153-8801","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022415231","display_name":"Antonio Algaba","orcid":"https://orcid.org/0000-0001-5872-7112"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Algaba","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014510689","display_name":"Alejandro J. Rodr\u00edguez-Luis","orcid":"https://orcid.org/0000-0002-9959-0789"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. J. Rodr\u00edguez-Luis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9959-0789","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2289,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92058414,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"1","first_page":"403","last_page":"437"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.995199978351593,"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":0.9914000034332275,"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/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.8113002181053162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7377604842185974},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.6477870941162109},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.6146942377090454},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6076622605323792},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.5774918794631958},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5127714276313782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49878573417663574},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.49060288071632385},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.333540141582489},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.33306777477264404},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.26100870966911316},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09508296847343445}],"concepts":[{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.8113002181053162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7377604842185974},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.6477870941162109},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.6146942377090454},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6076622605323792},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.5774918794631958},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5127714276313782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49878573417663574},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.49060288071632385},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.333540141582489},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.33306777477264404},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.26100870966911316},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09508296847343445},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1325101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1325101","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/high-order-approximation-of-heteroclinic-bifurcations-in-truncate","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:pure.atira.dk:publications/8a4386c9-f7a6-4b7d-b818-ae2dc0d7c51e","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/8a4386c9-f7a6-4b7d-b818-ae2dc0d7c51e","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Qin, B W, Chung, K W, Algaba, A & Rodriguez-Luis, A J 2021, 'High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities', SIAM Journal on Applied Dynamical Systems, vol. 20, no. 1, pp. 403-437. https://doi.org/10.1137/20M1325101","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/high-order-approximation-of-heteroclinic-bifurcations-in-truncate","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1529896857","display_name":null,"funder_award_id":"UHU-1260150","funder_id":"https://openalex.org/F4320321562","funder_display_name":"Consejer\u00eda de Econom\u00eda, Innovaci\u00f3n, Ciencia y Empleo, Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G1649059397","display_name":null,"funder_award_id":"2019173","funder_id":"https://openalex.org/F4320325570","funder_display_name":"Shanghai Municipal Human Resources and Social Security Bureau"},{"id":"https://openalex.org/G1825173035","display_name":null,"funder_award_id":"P12-FQM-1658","funder_id":"https://openalex.org/F4320321562","funder_display_name":"Consejer\u00eda de Econom\u00eda, Innovaci\u00f3n, Ciencia y Empleo, Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G2309484515","display_name":null,"funder_award_id":"FQM-276","funder_id":"https://openalex.org/F4320321562","funder_display_name":"Consejer\u00eda de Econom\u00eda, Innovaci\u00f3n, Ciencia y Empleo, Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G2326198362","display_name":null,"funder_award_id":"2020M670965","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4664384973","display_name":null,"funder_award_id":"PGC2018-096265-B-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G6895130789","display_name":null,"funder_award_id":"Nos 12001110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G793355291","display_name":null,"funder_award_id":"7004848","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G8168033335","display_name":null,"funder_award_id":"TIC-0130","funder_id":"https://openalex.org/F4320321562","funder_display_name":"Consejer\u00eda de Econom\u00eda, Innovaci\u00f3n, Ciencia y Empleo, Junta de Andaluc\u00eda"},{"id":"https://openalex.org/G8467973556","display_name":null,"funder_award_id":"MTM2017-87915-C2-1-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320321562","display_name":"Consejer\u00eda de Econom\u00eda, Innovaci\u00f3n, Ciencia y Empleo, Junta de Andaluc\u00eda","ror":"https://ror.org/03kak1729"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320325570","display_name":"Shanghai Municipal Human Resources and Social Security Bureau","ror":"https://ror.org/00zp3kj13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W9726823","https://openalex.org/W84041004","https://openalex.org/W125433455","https://openalex.org/W821701945","https://openalex.org/W1646660925","https://openalex.org/W1677009208","https://openalex.org/W1862031973","https://openalex.org/W1971156474","https://openalex.org/W1978787160","https://openalex.org/W1982912308","https://openalex.org/W1987061578","https://openalex.org/W1989110405","https://openalex.org/W1990614257","https://openalex.org/W1991665978","https://openalex.org/W1991890887","https://openalex.org/W2003334682","https://openalex.org/W2017671397","https://openalex.org/W2018136604","https://openalex.org/W2022211455","https://openalex.org/W2023058726","https://openalex.org/W2033477867","https://openalex.org/W2038472812","https://openalex.org/W2053439704","https://openalex.org/W2055816894","https://openalex.org/W2058567340","https://openalex.org/W2061636103","https://openalex.org/W2063646186","https://openalex.org/W2067245612","https://openalex.org/W2072561708","https://openalex.org/W2078266489","https://openalex.org/W2079371292","https://openalex.org/W2083689979","https://openalex.org/W2088254080","https://openalex.org/W2089643780","https://openalex.org/W2089655837","https://openalex.org/W2094913794","https://openalex.org/W2097835225","https://openalex.org/W2099533877","https://openalex.org/W2100850487","https://openalex.org/W2131274615","https://openalex.org/W2158977328","https://openalex.org/W2163931868","https://openalex.org/W2205246192","https://openalex.org/W2293945336","https://openalex.org/W2331926411","https://openalex.org/W2751521595","https://openalex.org/W2803873573","https://openalex.org/W2886068487","https://openalex.org/W2890492950","https://openalex.org/W2914949574","https://openalex.org/W2939676003","https://openalex.org/W2948873932","https://openalex.org/W2951295868","https://openalex.org/W2972651613","https://openalex.org/W2997071972","https://openalex.org/W3002216362","https://openalex.org/W3004739348","https://openalex.org/W3005656459","https://openalex.org/W3014048352","https://openalex.org/W3021034181","https://openalex.org/W3098446760","https://openalex.org/W3105902102","https://openalex.org/W3106197662","https://openalex.org/W4247616255"],"related_works":["https://openalex.org/W2151523878","https://openalex.org/W2049546479","https://openalex.org/W2233510040","https://openalex.org/W2052180011","https://openalex.org/W1497977526","https://openalex.org/W2008693397","https://openalex.org/W4300116311","https://openalex.org/W2346673812","https://openalex.org/W1965452729","https://openalex.org/W2963626261"],"abstract_inverted_index":{"Based":[0],"on":[1],"the":[2,55,58,63,68,71,80,85,93,110,118,140,145,158,175],"nonlinear":[3],"time":[4],"transformation":[5],"method,":[6],"in":[7,62,70,109,117,130,144,150,165,170,181],"this":[8],"paper":[9],"we":[10,89],"propose":[11],"a":[12,27,113],"recursive":[13],"algorithm":[14],"for":[15,26,54,67],"arbitrary":[16],"order":[17],"approximation":[18,47],"of":[19,30,35,84,121,132,174],"heteroclinic":[20,59,114],"orbits.":[21],"This":[22],"approach":[23],"works":[24],"fine":[25],"wide":[28],"class":[29],"systems":[31],"that":[32,78,157],"are":[33,128,148],"perturbations":[34],"non-Hamiltonian":[36],"integrable":[37],"planar":[38],"vector":[39],"fields.":[40],"Specifically,":[41],"our":[42],"method":[43],"can":[44,161],"provide":[45],"an":[46,105],"up":[48],"to":[49,92,104],"any":[50],"desired":[51],"order,":[52],"both":[53],"locus":[56],"where":[57,112],"bifurcation":[60,107],"occurs":[61],"parameter":[64],"space":[65],"and":[66,82,96],"orbit":[69],"phase":[72],"space.":[73],"We":[74],"also":[75,149],"give":[76,102],"proofs":[77],"guarantee":[79],"existence":[81],"uniqueness":[83],"solution.":[86],"As":[87],"illustrations,":[88],"apply":[90],"it":[91],"generic":[94],"Hopf-zero":[95],"nonresonant":[97],"double":[98],"Hopf":[99],"singularities":[100],"which":[101,138,171],"rise":[103],"intricate":[106],"scenario":[108],"cases":[111],"cycle":[115],"appears":[116],"corresponding":[119],"unfolding":[120],"normal":[122,135],"forms.":[123],"The":[124],"obtained":[125],"high-order":[126],"approximations":[127,143],"expressed":[129],"terms":[131],"symbolic":[133],"nonzero":[134],"form":[136],"coefficients":[137],"improve":[139],"existing":[141],"first-order":[142],"literature.":[146],"They":[147],"excellent":[151],"agreement":[152],"with":[153],"numerical":[154],"continuations.":[155],"Note":[156],"derived":[159],"formulas":[160],"be":[162,179],"practically":[163],"important":[164],"many":[166],"control":[167],"engineering":[168],"applications":[169],"certain":[172],"constants":[173],"problem":[176],"may":[177],"not":[178],"known":[180],"advance.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-08-09T07:27:16.801131","created_date":"2025-09-05T00:00:00"}