{"id":"https://openalex.org/W4308438246","doi":"https://doi.org/10.1142/s0218127422502017","title":"Global Dynamics of a Planar Piecewise Linear Refracting System of Node-Node Types","display_name":"Global Dynamics of a Planar Piecewise Linear Refracting System of Node-Node Types","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W4308438246","doi":"https://doi.org/10.1142/s0218127422502017"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422502017","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422502017","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/A5050444824","display_name":"Hefei Zhao","orcid":"https://orcid.org/0000-0003-1988-7230"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hefei Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang 550025, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, P. R. China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025837333","display_name":"Kuilin Wu","orcid":"https://orcid.org/0000-0001-5872-3808"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kuilin Wu","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang 550025, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, P. R. China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067453293","display_name":"Yi Shao","orcid":"https://orcid.org/0000-0001-5721-7874"},"institutions":[{"id":"https://openalex.org/I183816158","display_name":"Zhaoqing University","ror":"https://ror.org/025n5kj18","country_code":"CN","type":"education","lineage":["https://openalex.org/I183816158"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Shao","raw_affiliation_strings":["School of Mathematics and Statistics, Zhaoqing University, Guangdong 526061, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-5721-7874","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhaoqing University, Guangdong 526061, P. R. China","institution_ids":["https://openalex.org/I183816158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5629,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82515315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"32","issue":"13","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":1.0,"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":1.0,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9661999940872192,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9624999761581421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.7390027046203613},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.6256641745567322},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6081809997558594},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5746278762817383},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5620119571685791},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.548534631729126},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.46465176343917847},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4628618657588959},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4586198031902313},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4577315151691437},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.42730244994163513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2914159297943115},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.27741163969039917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2660301923751831},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23923635482788086},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.17822101712226868},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16719090938568115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11486288905143738}],"concepts":[{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.7390027046203613},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.6256641745567322},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6081809997558594},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5746278762817383},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5620119571685791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.548534631729126},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.46465176343917847},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4628618657588959},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4586198031902313},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4577315151691437},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.42730244994163513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2914159297943115},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.27741163969039917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2660301923751831},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23923635482788086},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.17822101712226868},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16719090938568115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11486288905143738},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127422502017","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422502017","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/G121207363","display_name":"\u6709\u5173\u963f\u8d1d\u5c14\u79ef\u5206\u7684\u51e0\u4e2a\u95ee\u9898\u7814\u7a76","funder_award_id":"11661017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7837625050","display_name":null,"funder_award_id":"ZK[2022]G118","funder_id":"https://openalex.org/F4320336617","funder_display_name":"Science and Technology Program of Guizhou Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336617","display_name":"Science and Technology Program of Guizhou Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W618523876","https://openalex.org/W1515307033","https://openalex.org/W1547590019","https://openalex.org/W1552277675","https://openalex.org/W1850403730","https://openalex.org/W1968084142","https://openalex.org/W1974272814","https://openalex.org/W1980228211","https://openalex.org/W2002282594","https://openalex.org/W2002695016","https://openalex.org/W2009511821","https://openalex.org/W2009968757","https://openalex.org/W2012681042","https://openalex.org/W2017234121","https://openalex.org/W2050710621","https://openalex.org/W2053658423","https://openalex.org/W2054652000","https://openalex.org/W2066824120","https://openalex.org/W2068536407","https://openalex.org/W2072652000","https://openalex.org/W2073072471","https://openalex.org/W2163668399","https://openalex.org/W2526407710","https://openalex.org/W2889668533","https://openalex.org/W2922368149","https://openalex.org/W2980852070","https://openalex.org/W2981530608","https://openalex.org/W3031244554","https://openalex.org/W3090096152","https://openalex.org/W3149668445","https://openalex.org/W3181518534","https://openalex.org/W4242340741"],"related_works":["https://openalex.org/W2086965780","https://openalex.org/W2358352735","https://openalex.org/W2119154230","https://openalex.org/W2951830210","https://openalex.org/W3147887110","https://openalex.org/W4281713759","https://openalex.org/W2061663685","https://openalex.org/W2039889532","https://openalex.org/W4280562183","https://openalex.org/W1965781123"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"global":[5],"dynamics":[6],"of":[7,18,20,36,41,44,51],"a":[8,15],"planar":[9],"piecewise":[10],"linear":[11],"refracting":[12,46],"system":[13,47],"with":[14],"straight":[16],"line":[17],"separation":[19],"node-node":[21,29],"type,":[22,30],"improper":[23,28],"node-improper":[24],"node":[25],"type":[26],"and":[27,39,48],"respectively.":[31],"We":[32],"obtain":[33],"the":[34,37,45,52,57],"conditions":[35],"uniqueness":[38],"nonexistence":[40],"limit":[42],"cycles":[43],"provide":[49],"classifications":[50],"topological":[53],"phase":[54],"portraits":[55],"in":[56],"Poincar\u00e9":[58],"disk.":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}