{"id":"https://openalex.org/W1970615721","doi":"https://doi.org/10.1142/s0218127409023603","title":"SADDLE QUANTITIES AND CYCLICITY OF 2-POLYCYCLE","display_name":"SADDLE QUANTITIES AND CYCLICITY OF 2-POLYCYCLE","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W1970615721","doi":"https://doi.org/10.1142/s0218127409023603","mag":"1970615721"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409023603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023603","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/A5101684735","display_name":"Liqin Zhao","orcid":"https://orcid.org/0009-0007-5008-2621"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LIQIN ZHAO","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081848844","display_name":"Xuexing Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XUEXING WANG","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07190743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"04","first_page":"1255","last_page":"1266"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9843999743461609,"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/T11844","display_name":"Lipid metabolism and biosynthesis","score":0.9668999910354614,"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/saddle","display_name":"Saddle","score":0.8746113777160645},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7443717122077942},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7038992047309875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5980912446975708},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5753964781761169},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5695337653160095},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.49308130145072937},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48352503776550293},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.4668738543987274},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23400503396987915},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17111581563949585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.14119881391525269}],"concepts":[{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.8746113777160645},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7443717122077942},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7038992047309875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5980912446975708},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5753964781761169},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5695337653160095},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.49308130145072937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48352503776550293},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.4668738543987274},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23400503396987915},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17111581563949585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.14119881391525269},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/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/s0218127409023603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023603","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W135561972","https://openalex.org/W1141904788","https://openalex.org/W1564263151","https://openalex.org/W1963615000","https://openalex.org/W1964728923","https://openalex.org/W2001428827","https://openalex.org/W2009734469","https://openalex.org/W2023533391","https://openalex.org/W2024356403","https://openalex.org/W2034444332","https://openalex.org/W2042498362","https://openalex.org/W2061809639","https://openalex.org/W2069228691","https://openalex.org/W2077189269","https://openalex.org/W2078286309","https://openalex.org/W2142664960","https://openalex.org/W2321988677","https://openalex.org/W2324297661","https://openalex.org/W2584645706"],"related_works":["https://openalex.org/W4225624922","https://openalex.org/W3215350949","https://openalex.org/W4312314483","https://openalex.org/W2046214901","https://openalex.org/W2270304941","https://openalex.org/W2105534223","https://openalex.org/W2613793204","https://openalex.org/W4385564864","https://openalex.org/W2317542160","https://openalex.org/W2783708856"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,8,40],"bifurcation":[3],"of":[4,10,31],"limit":[5],"cycles":[6],"in":[7],"neighborhood":[9],"a":[11],"2-polycycle":[12],"through":[13],"two":[14],"hyperbolic":[15],"saddles":[16],"with":[17],"both":[18,43],"hyperbolicity":[19],"ratios":[20],"being":[21],"1.":[22],"The":[23],"cyclicity":[24],"is":[25],"expressed":[26],"as":[27],"an":[28],"explicit":[29],"function":[30],"saddle":[32],"quantities.":[33],"Our":[34],"results":[35],"can":[36],"be":[37],"applied":[38],"to":[39],"case":[41],"when":[42],"connections":[44],"are":[45],"broken":[46],"under":[47],"perturbations.":[48]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
