{"id":"https://openalex.org/W2157753588","doi":"https://doi.org/10.1142/s0218127413500272","title":"THE STABILITY OF SOME KINDS OF GENERALIZED HOMOCLINIC LOOPS IN PLANAR PIECEWISE SMOOTH SYSTEMS","display_name":"THE STABILITY OF SOME KINDS OF GENERALIZED HOMOCLINIC LOOPS IN PLANAR PIECEWISE SMOOTH SYSTEMS","publication_year":2013,"publication_date":"2013-02-01","ids":{"openalex":"https://openalex.org/W2157753588","doi":"https://doi.org/10.1142/s0218127413500272","mag":"2157753588"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500272","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500272","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/A5101923436","display_name":"Feng Liang","orcid":"https://orcid.org/0000-0001-6305-6886"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FENG LIANG","raw_affiliation_strings":["The Institute of Mathematics, Anhui Normal University, South Huajin Road 2, Wuhu 241000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematics, Anhui Normal University, South Huajin Road 2, Wuhu 241000, P. R. China","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"MAOAN HAN","raw_affiliation_strings":["The Institute of Mathematics, Shanghai Normal University, Guilin Road 100, Shanghai 200234, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematics, Shanghai Normal University, Guilin Road 100, Shanghai 200234, P. R. China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030649439"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":1.3439,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8110251,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"02","first_page":"1350027","last_page":"1350027"},"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":0.987500011920929,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9723954200744629},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7975637316703796},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7797546982765198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.745074450969696},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7193363904953003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4351123571395874},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4011557400226593},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38545936346054077},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.15099292993545532},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14663368463516235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14083737134933472},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0871042013168335},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.05692005157470703}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9723954200744629},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7975637316703796},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7797546982765198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.745074450969696},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7193363904953003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4351123571395874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4011557400226593},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38545936346054077},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.15099292993545532},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14663368463516235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14083737134933472},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0871042013168335},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.05692005157470703},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413500272","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500272","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":[{"id":"https://metadata.un.org/sdg/11","score":0.7200000286102295,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1592648094","https://openalex.org/W2001428827","https://openalex.org/W2053658423","https://openalex.org/W2078512508","https://openalex.org/W2079151093","https://openalex.org/W2104958104","https://openalex.org/W2224899793"],"related_works":["https://openalex.org/W2363992932","https://openalex.org/W2043723919","https://openalex.org/W2066340280","https://openalex.org/W1999123830","https://openalex.org/W2971991931","https://openalex.org/W2054807178","https://openalex.org/W2759184667","https://openalex.org/W4200274144","https://openalex.org/W2028231540","https://openalex.org/W2044983663"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,20],"present":[4],"some":[5],"kinds":[6],"of":[7,24],"generalized":[8,25],"homoclinic":[9,26],"loops":[10,27],"in":[11],"planar":[12],"piecewise":[13,43],"smooth":[14],"systems.":[15],"By":[16],"establishing":[17],"Poincar\u00e9":[18],"map,":[19],"study":[21],"the":[22],"stability":[23],"for":[28,35],"each":[29],"case.":[30],"Some":[31],"criteria":[32],"are":[33,45],"given":[34],"their":[36],"stability,":[37],"respectively.":[38],"As":[39],"applications,":[40],"several":[41],"concrete":[42],"systems":[44],"considered.":[46]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
