{"id":"https://openalex.org/W4411769273","doi":"https://doi.org/10.1142/s0218127425501329","title":"Bifurcations of Double Critical Homoclinic Loops Connecting One Tangent Point","display_name":"Bifurcations of Double Critical Homoclinic Loops Connecting One Tangent Point","publication_year":2025,"publication_date":"2025-06-27","ids":{"openalex":"https://openalex.org/W4411769273","doi":"https://doi.org/10.1142/s0218127425501329"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425501329","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501329","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/A5067043218","display_name":"Zhihao Fang","orcid":"https://orcid.org/0009-0006-0634-4383"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihao Fang","raw_affiliation_strings":["School of Mathematics, Sichuan University, Chengdu, Sichuan 610065, P. R. China"],"raw_orcid":"https://orcid.org/0009-0006-0634-4383","affiliations":[{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, Sichuan 610065, P. R. China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":null,"display_name":"Xingwu Chen","orcid":"https://orcid.org/0000-0002-1450-0503"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210110609","display_name":"Chongqing University of Arts and Sciences","ror":"https://ror.org/01rcvq140","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110609"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingwu Chen","raw_affiliation_strings":["School of Mathematics and Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China","School of Mathematics, Sichuan University, Chengdu, Sichuan 610065, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-1450-0503","affiliations":[{"raw_affiliation_string":"School of Mathematics and Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China","institution_ids":["https://openalex.org/I4210110609"]},{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, Sichuan 610065, P. R. China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067043218"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":null,"apc_paid":null,"fwci":3.7675,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.90828402,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"35","issue":"11","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11844","display_name":"Lipid metabolism and biosynthesis","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/1303","display_name":"Biochemistry"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9365034699440002},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.7239611744880676},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6488710641860962},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.550310492515564},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.5479949116706848},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.54515141248703},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.5387862920761108},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.5005979537963867},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4200098514556885},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.41368716955184937},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4060332775115967},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2553592622280121},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23834842443466187},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.188298761844635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18084308505058289}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9365034699440002},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7239611744880676},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6488710641860962},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.550310492515564},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.5479949116706848},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.54515141248703},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.5387862920761108},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.5005979537963867},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4200098514556885},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.41368716955184937},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4060332775115967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2553592622280121},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23834842443466187},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.188298761844635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18084308505058289},{"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/s0218127425501329","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501329","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":[{"id":"https://openalex.org/G3101690337","display_name":null,"funder_award_id":"12271378","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"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":28,"referenced_works":["https://openalex.org/W1269033259","https://openalex.org/W1557324374","https://openalex.org/W1596321532","https://openalex.org/W1974272814","https://openalex.org/W2006943190","https://openalex.org/W2047449028","https://openalex.org/W2083823140","https://openalex.org/W2083933571","https://openalex.org/W2087081695","https://openalex.org/W2089466166","https://openalex.org/W2133505353","https://openalex.org/W2778531943","https://openalex.org/W2883913766","https://openalex.org/W2888615804","https://openalex.org/W2985237850","https://openalex.org/W3089267081","https://openalex.org/W3162840096","https://openalex.org/W3169457090","https://openalex.org/W3195243666","https://openalex.org/W3208535967","https://openalex.org/W4293078920","https://openalex.org/W4310346317","https://openalex.org/W4383045267","https://openalex.org/W4388439153","https://openalex.org/W4404875221","https://openalex.org/W4404994713","https://openalex.org/W4406486812","https://openalex.org/W4406731724"],"related_works":["https://openalex.org/W2890492950","https://openalex.org/W2010606039","https://openalex.org/W3115184012","https://openalex.org/W352136236","https://openalex.org/W944345475","https://openalex.org/W2045215015","https://openalex.org/W2356323067","https://openalex.org/W2363270381","https://openalex.org/W1056177206","https://openalex.org/W2049818805"],"abstract_inverted_index":{"In":[0],"this":[1,22],"paper,":[2],"we":[3,116],"investigate":[4],"the":[5,33,58,61,68,84,87,118,121],"bifurcations":[6,110],"of":[7,28,60,71,111,120],"a":[8,99,103],"double":[9,23,62],"critical":[10,30,55,89],"homoclinic":[11,24,63],"loop":[12,25],"connecting":[13,32],"one":[14],"tangent":[15,35],"point":[16],"in":[17,83],"piecewise-smooth":[18],"differential":[19],"systems.":[20],"Since":[21],"is":[26,81],"composed":[27],"two":[29,54,88],"loops":[31,44,56,77,90],"same":[34],"point,":[36],"there":[37],"are":[38,91],"crossing":[39,72],"limit":[40,73],"cycles":[41,74],"and":[42,57,75,93,124,129],"sliding":[43,76],"simultaneously":[45],"bifurcating":[46],"from":[47,53],"three":[48,113],"parts":[49,114],"under":[50,78],"perturbations,":[51],"i.e.":[52],"exterior":[59],"loop.":[64],"We":[65],"prove":[66,117],"that":[67,86],"maximum":[69,122],"sum":[70,123],"any":[79],"perturbations":[80],"5":[82],"case":[85],"unstable,":[92],"4":[94],"otherwise.":[95],"Further,":[96],"by":[97],"constructing":[98],"perturbation":[100],"system":[101],"with":[102],"three-dimensional":[104],"unfolding":[105],"parameter":[106],"which":[107],"independently":[108],"controls":[109],"these":[112],"separately,":[115],"reachability":[119],"obtain":[125],"their":[126],"coexistence":[127],"numbers":[128],"locations.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}