{"id":"https://openalex.org/W3005993020","doi":"https://doi.org/10.1109/access.2020.2973469","title":"Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function","display_name":"Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3005993020","doi":"https://doi.org/10.1109/access.2020.2973469","mag":"3005993020"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.2973469","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2973469","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08995544.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08995544.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100444422","display_name":"Wen Zhang","orcid":"https://orcid.org/0000-0003-2293-099X"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Zhang","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075406368","display_name":"Fuhong Min","orcid":"https://orcid.org/0000-0001-7826-3124"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuhong Min","raw_affiliation_strings":["Jiangsu Key Laboratory of New Power Batteries, Nanjing Normal University, Nanjing, China","School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-7826-3124","affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory of New Power Batteries, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101709925","display_name":"Jiayun Chen","orcid":"https://orcid.org/0000-0003-2927-7647"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiayun Chen","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109737908","display_name":"Yiping Dou","orcid":null},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiping Dou","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.5342,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6219224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"8","issue":null,"first_page":"32312","last_page":"32320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9997000098228455,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9993000030517578,"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":0.9983000159263611,"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/piecewise","display_name":"Piecewise","score":0.7708179950714111},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6208867430686951},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5847228169441223},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5696529746055603},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5349401831626892},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5206300616264343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5071771144866943},{"id":"https://openalex.org/keywords/rayleigh-scattering","display_name":"Rayleigh scattering","score":0.4711809456348419},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4531285762786865},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4525623917579651},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.44539642333984375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4356403052806854},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.4244970381259918},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.41732341051101685},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29549646377563477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20017051696777344},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16255223751068115},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12691974639892578}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7708179950714111},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6208867430686951},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5847228169441223},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5696529746055603},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5349401831626892},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5206300616264343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5071771144866943},{"id":"https://openalex.org/C46244369","wikidata":"https://www.wikidata.org/wiki/Q193709","display_name":"Rayleigh scattering","level":2,"score":0.4711809456348419},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4531285762786865},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4525623917579651},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.44539642333984375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4356403052806854},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.4244970381259918},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.41732341051101685},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29549646377563477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20017051696777344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16255223751068115},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12691974639892578},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.2973469","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2973469","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08995544.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b983a1c534d4428c8ede5c0c3d8d5934","is_oa":true,"landing_page_url":"https://doaj.org/article/b983a1c534d4428c8ede5c0c3d8d5934","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 32312-32320 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.2973469","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2973469","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08995544.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1993483461","display_name":"\u5fc6\u963b\u7535\u8def\u590d\u6742\u632f\u8361\u7684\u51e0\u4f55\u4e0e\u5206\u5e03\u8c03\u63a7\u7814\u7a76","funder_award_id":"61871230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4627539250","display_name":"\u975e\u5149\u6ed1\u5fc6\u963b\u7cfb\u7edf\u7684\u8fb9\u754c\u632f\u8361\u884c\u4e3a\u4e0e\u5207\u6362\u540c\u6b65\u7814\u7a76","funder_award_id":"61971228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4830209077","display_name":null,"funder_award_id":"19KJB520042","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"},{"id":"https://openalex.org/G661680406","display_name":"\u6c30\u80f6\u6cd5\u5236\u5907\u951a\u5b9a\u578b\u591a\u5b54\u78b3\u57fa\u8fc7\u6e21\u91d1\u5c5e\u53cc\u529f\u80fd\u7a7a\u6c14\u7535\u6781\u53ca\u5176\u6027\u80fd\u7814\u7a76","funder_award_id":"21875112","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"},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3005993020.pdf","grobid_xml":"https://content.openalex.org/works/W3005993020.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1542389835","https://openalex.org/W1804335063","https://openalex.org/W1969774171","https://openalex.org/W1974611126","https://openalex.org/W2024198800","https://openalex.org/W2026823472","https://openalex.org/W2042946512","https://openalex.org/W2046051520","https://openalex.org/W2046811681","https://openalex.org/W2050732796","https://openalex.org/W2053608746","https://openalex.org/W2065458999","https://openalex.org/W2081016193","https://openalex.org/W2088458865","https://openalex.org/W2098011797","https://openalex.org/W2158249558","https://openalex.org/W2265063183","https://openalex.org/W2508268974","https://openalex.org/W2521453462","https://openalex.org/W2543919710","https://openalex.org/W2592975237","https://openalex.org/W2745041239","https://openalex.org/W2765165617","https://openalex.org/W2965150913","https://openalex.org/W2966371685","https://openalex.org/W2969006849"],"related_works":["https://openalex.org/W3198888254","https://openalex.org/W2054889292","https://openalex.org/W2045969073","https://openalex.org/W2368165912","https://openalex.org/W2350371552","https://openalex.org/W1760827084","https://openalex.org/W2093909018","https://openalex.org/W2044646666","https://openalex.org/W2147537746","https://openalex.org/W1983551025"],"abstract_inverted_index":{"The":[0,16,52,73],"discontinuous":[1,34],"dynamical":[2,35],"behavior":[3],"of":[4,33,54,88,101],"a":[5,10,85],"modified":[6],"Duffing-Rayleigh":[7],"system":[8,57],"with":[9,78],"piecewise":[11],"quadratic":[12],"function":[13],"is":[14,62],"studied.":[15],"necessary":[17],"and":[18,48,67,75],"sufficient":[19],"conditions":[20,61],"for":[21,84],"motion":[22,90],"switchability":[23],"at":[24],"the":[25,31,40,45,68,89,95,99,102],"velocity":[26],"boundary":[27,41],"are":[28,42,82],"investigated":[29],"through":[30,39],"theory":[32],"systems.":[36],"Various":[37],"motions":[38,77],"demonstrated":[43],"by":[44,64],"parameter":[46],"maps":[47],"coexisting":[49],"bifurcation":[50],"diagrams.":[51],"coexistence":[53],"an":[55],"example":[56],"under":[58],"different":[59,79],"initial":[60],"illustrated":[63],"attraction":[65],"basins,":[66],"trajectories":[69],"in":[70],"phase":[71],"plane.":[72],"periodic":[74],"chaotic":[76],"mapping":[80],"structures":[81],"analyzed":[83],"better":[86],"understanding":[87],"switching":[91],"mechanism.":[92],"Through":[93],"Multisim,":[94],"circuit":[96],"experiment":[97],"proves":[98],"effectiveness":[100],"theoretical":[103],"analysis.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}