{"id":"https://openalex.org/W3082147466","doi":"https://doi.org/10.1142/s0218127420501412","title":"Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities","display_name":"Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities","publication_year":2020,"publication_date":"2020-08-01","ids":{"openalex":"https://openalex.org/W3082147466","doi":"https://doi.org/10.1142/s0218127420501412","mag":"3082147466"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501412","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/A5112560977","display_name":"R. L. Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I90090648","display_name":"Shijiazhuang Tiedao University","ror":"https://ror.org/022e9e065","country_code":"CN","type":"education","lineage":["https://openalex.org/I90090648"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"R. L. Tian","raw_affiliation_strings":["Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-4538-9094","affiliations":[{"raw_affiliation_string":"Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","institution_ids":[]},{"raw_affiliation_string":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100428420","display_name":"Tian Wang","orcid":"https://orcid.org/0009-0000-2022-3592"},"institutions":[{"id":"https://openalex.org/I90090648","display_name":"Shijiazhuang Tiedao University","ror":"https://ror.org/022e9e065","country_code":"CN","type":"education","lineage":["https://openalex.org/I90090648"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"T. Wang","raw_affiliation_strings":["Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","institution_ids":[]},{"raw_affiliation_string":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019469769","display_name":"Yufeng Zhou","orcid":"https://orcid.org/0000-0002-9683-6333"},"institutions":[{"id":"https://openalex.org/I90090648","display_name":"Shijiazhuang Tiedao University","ror":"https://ror.org/022e9e065","country_code":"CN","type":"education","lineage":["https://openalex.org/I90090648"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Y. F. Zhou","raw_affiliation_strings":["Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China","institution_ids":[]},{"raw_affiliation_string":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]},{"raw_affiliation_string":"Key Laboratory of Smart Materials and Structures Mechanics, Hebei Province, 050043, P. R. China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China","institution_ids":["https://openalex.org/I90090648"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047717019","display_name":"J. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"J. Li","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051589309","display_name":"Shaotao Zhu","orcid":"https://orcid.org/0000-0002-5670-8986"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"S. T. Zhu","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5112560977"],"corresponding_institution_ids":["https://openalex.org/I90090648"],"apc_list":null,"apc_paid":null,"fwci":1.8694,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.8570162,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"10","first_page":"2050141","last_page":"2050141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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/T10244","display_name":"Chaos control and synchronization","score":0.9991999864578247,"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":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9070464372634888},{"id":"https://openalex.org/keywords/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.8256232142448425},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.7342421412467957},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6699679493904114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6555526852607727},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.582960844039917},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5390675663948059},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4996936321258545},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.46542900800704956},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4376141428947449},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1356005072593689},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12501215934753418},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.11733308434486389},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06159687042236328}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9070464372634888},{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.8256232142448425},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.7342421412467957},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6699679493904114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6555526852607727},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.582960844039917},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5390675663948059},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4996936321258545},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.46542900800704956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4376141428947449},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1356005072593689},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12501215934753418},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.11733308434486389},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06159687042236328},{"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/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"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/s0218127420501412","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501412","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/G2084046426","display_name":null,"funder_award_id":"11790282","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5571602865","display_name":null,"funder_award_id":"(Nos. 11872253","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6247504843","display_name":"\u51e0\u7c7b\u9ad8\u7ef4\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u591a\u5468\u671f\u89e3\u5206\u5c94\u7684\u7814\u7a76\u53ca\u5e94\u7528","funder_award_id":"11772007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8490138949","display_name":null,"funder_award_id":"11602151","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1593811304","https://openalex.org/W1949487648","https://openalex.org/W1994853181","https://openalex.org/W1995320774","https://openalex.org/W2006193357","https://openalex.org/W2010965181","https://openalex.org/W2031320505","https://openalex.org/W2041192585","https://openalex.org/W2050416508","https://openalex.org/W2058647515","https://openalex.org/W2079633489","https://openalex.org/W2083958116","https://openalex.org/W2139227403","https://openalex.org/W2141431977","https://openalex.org/W2164297166","https://openalex.org/W2280495112","https://openalex.org/W2316649394","https://openalex.org/W2342787669","https://openalex.org/W2485241328","https://openalex.org/W2518000080","https://openalex.org/W2606732085","https://openalex.org/W2762552577","https://openalex.org/W4238307931"],"related_works":["https://openalex.org/W2151523878","https://openalex.org/W1979395696","https://openalex.org/W2157317278","https://openalex.org/W2233510040","https://openalex.org/W2052180011","https://openalex.org/W2049546479","https://openalex.org/W1497977526","https://openalex.org/W2008693397","https://openalex.org/W4300116311","https://openalex.org/W2346673812"],"abstract_inverted_index":{"In":[0,34],"smooth":[1],"systems,":[2],"the":[3,6,16,65,69,72,75,79,82,89,98,106,115,118,126,129,134,149,152,160,163,173],"form":[4,150],"of":[5,15,46,74,81,117,128,136,151,162],"heteroclinic":[7,58,108,120,131,154],"Melnikov":[8,18,100,109,155,166,175],"chaotic":[9,19,110],"threshold":[10],"is":[11,50,102,144,157,169],"similar":[12],"to":[13,88,104,125],"that":[14,114,148],"homoclinic":[17,165],"threshold.":[20],"However,":[21],"this":[22,35],"conclusion":[23],"may":[24,122],"not":[25],"be":[26,94,123],"valid":[27],"in":[28],"nonsmooth":[29,42,57,76,83,107,119,130,141,153,164],"systems":[30],"with":[31,60],"jump":[32,62],"discontinuities.":[33,63],"paper,":[36],"based":[37],"on":[38,78],"a":[39,44,56],"newly":[40],"constructed":[41],"pendulum,":[43],"kind":[45],"impulsive":[47],"differential":[48],"system":[49,85],"introduced,":[51],"whose":[52],"unperturbed":[53],"part":[54],"possesses":[55],"solution":[59],"multiple":[61],"Using":[64],"recursive":[66],"method":[67],"and":[68,140],"perturbation":[70,135],"principle,":[71],"effects":[73],"factors":[77],"behaviors":[80],"dynamical":[84],"are":[86],"converted":[87],"integral":[90],"items":[91],"which":[92,112,168],"can":[93],"easily":[95],"calculated.":[96],"Furthermore,":[97],"extended":[99],"function":[101,156],"employed":[103],"obtain":[105],"threshold,":[111],"implies":[113],"existence":[116],"orbits":[121],"due":[124],"breaking":[127],"loops":[132],"under":[133],"damping,":[137],"external":[138],"forcing":[139],"factors.":[142],"It":[143],"worth":[145],"pointing":[146],"out":[147],"different":[158,171],"from":[159,172],"one":[161],"function,":[167],"quite":[170],"classical":[174],"theory.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":8}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
