{"id":"https://openalex.org/W2023319414","doi":"https://doi.org/10.1142/s021812741250112x","title":"NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP","display_name":"NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP","publication_year":2012,"publication_date":"2012-03-29","ids":{"openalex":"https://openalex.org/W2023319414","doi":"https://doi.org/10.1142/s021812741250112x","mag":"2023319414"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741250112x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250112x","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/A5039958108","display_name":"Zhiying Qin","orcid":null},"institutions":[{"id":"https://openalex.org/I34155123","display_name":"Hebei University of Science and Technology","ror":"https://ror.org/05h3pkk68","country_code":"CN","type":"education","lineage":["https://openalex.org/I34155123"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZHIYING QIN","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China","institution_ids":["https://openalex.org/I34155123"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100984923","display_name":"Yuejing Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I34155123","display_name":"Hebei University of Science and Technology","ror":"https://ror.org/05h3pkk68","country_code":"CN","type":"education","lineage":["https://openalex.org/I34155123"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YUEJING ZHAO","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China","institution_ids":["https://openalex.org/I34155123"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100823309","display_name":"Jichen Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JICHEN YANG","raw_affiliation_strings":["Department of Dynamics and Control, Beihang University, Beijing 100091, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Dynamics and Control, Beihang University, Beijing 100091, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.048,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85114081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"05","first_page":"1250112","last_page":"1250112"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9983999729156494,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7538765072822571},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.7524377107620239},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.7359213829040527},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7316944599151611},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6328362822532654},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.5905193090438843},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5858616828918457},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.5259361863136292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5247252583503723},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.47365009784698486},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.45052653551101685},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.44309818744659424},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.43562787771224976},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4336753189563751},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4129210412502289},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.20908334851264954},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10757645964622498}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7538765072822571},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.7524377107620239},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.7359213829040527},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7316944599151611},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6328362822532654},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.5905193090438843},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5858616828918457},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.5259361863136292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5247252583503723},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.47365009784698486},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.45052653551101685},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.44309818744659424},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.43562787771224976},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4336753189563751},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4129210412502289},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.20908334851264954},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10757645964622498},{"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/s021812741250112x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250112x","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":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2005988040","https://openalex.org/W2011227277","https://openalex.org/W2040317361","https://openalex.org/W2143976842","https://openalex.org/W2159251357","https://openalex.org/W2170408252","https://openalex.org/W4240452402"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W3020506472","https://openalex.org/W2775656422","https://openalex.org/W4245057904","https://openalex.org/W2025138898","https://openalex.org/W2325048728","https://openalex.org/W2978098199","https://openalex.org/W4281733204","https://openalex.org/W3081645617","https://openalex.org/W2054978396"],"abstract_inverted_index":{"In":[0],"this":[1,15],"paper,":[2],"a":[3,71],"piecewise":[4,16],"map":[5],"with":[6],"singularity":[7],"of":[8,29],"the":[9,25,84],"power":[10],"(-1/2)":[11],"is":[12,19,74],"introduced.":[13],"For":[14,42,58],"map,":[17],"there":[18,77],"an":[20],"infinite":[21],"discontinuous":[22],"gap":[23],"on":[24],"origin.":[26],"The":[27],"conditions":[28],"nonsmooth":[30],"border-collision":[31],"bifurcation":[32,38,56,62,86],"and":[33,70],"smooth":[34],"fold":[35],"or":[36],"flip":[37],"are":[39,78],"analytically":[40],"derived.":[41],"period-1":[43],"fixed":[44],"point,":[45],"two-parameter-plane":[46],"can":[47],"be":[48],"divided":[49],"into":[50],"seven":[51],"ranges":[52],"according":[53],"to":[54,66],"different":[55,67,80],"structures.":[57],"period-n":[59],"orbits,":[60],"codimension-2":[61],"point":[63],"may":[64],"lead":[65],"period-increment":[68,81],"sequence,":[69],"peculiar":[72],"feature":[73],"found":[75],"that":[76],"two":[79],"sequences":[82],"in":[83],"same":[85],"diagram.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
