{"id":"https://openalex.org/W3175369621","doi":"https://doi.org/10.1142/s0218127421300226","title":"Slow\u2013Fast Behaviors and Their Mechanism in a Periodically Excited Dynamical System with Double Hopf Bifurcations","display_name":"Slow\u2013Fast Behaviors and Their Mechanism in a Periodically Excited Dynamical System with Double Hopf Bifurcations","publication_year":2021,"publication_date":"2021-06-26","ids":{"openalex":"https://openalex.org/W3175369621","doi":"https://doi.org/10.1142/s0218127421300226","mag":"3175369621"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421300226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300226","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/A5102728048","display_name":"Miaorong Zhang","orcid":"https://orcid.org/0000-0002-0953-8144"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miaorong Zhang","raw_affiliation_strings":["Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100782561","display_name":"Xiaofang Zhang","orcid":"https://orcid.org/0000-0002-3854-5423"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaofang Zhang","raw_affiliation_strings":["Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000921390","display_name":"Qinsheng Bi","orcid":"https://orcid.org/0000-0002-1058-7154"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qinsheng Bi","raw_affiliation_strings":["Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-1058-7154","affiliations":[{"raw_affiliation_string":"Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000921390"],"corresponding_institution_ids":["https://openalex.org/I115592961"],"apc_list":null,"apc_paid":null,"fwci":1.3118,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80452389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"08","first_page":"2130022","last_page":"2130022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998000264167786,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998000264167786,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.995199978351593,"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/attractor","display_name":"Attractor","score":0.7322514653205872},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6972853541374207},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.6384767293930054},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5844504833221436},{"id":"https://openalex.org/keywords/bursting","display_name":"Bursting","score":0.5699265003204346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5236979722976685},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4767816364765167},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.47375115752220154},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4523729085922241},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4459910988807678},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.445549339056015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42355769872665405},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3903394341468811},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3354093134403229},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12232780456542969},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10176047682762146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08302196860313416}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7322514653205872},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6972853541374207},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.6384767293930054},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5844504833221436},{"id":"https://openalex.org/C195221683","wikidata":"https://www.wikidata.org/wiki/Q5000649","display_name":"Bursting","level":2,"score":0.5699265003204346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5236979722976685},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4767816364765167},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.47375115752220154},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4523729085922241},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4459910988807678},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.445549339056015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42355769872665405},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3903394341468811},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3354093134403229},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12232780456542969},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10176047682762146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08302196860313416},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421300226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300226","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/G7388677852","display_name":null,"funder_award_id":"11632008","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W10447158","https://openalex.org/W1964294610","https://openalex.org/W1973827406","https://openalex.org/W1984097237","https://openalex.org/W1985119234","https://openalex.org/W1985940938","https://openalex.org/W1991641752","https://openalex.org/W2006504966","https://openalex.org/W2011845888","https://openalex.org/W2027004361","https://openalex.org/W2034765981","https://openalex.org/W2089838023","https://openalex.org/W2095110157","https://openalex.org/W2098267860","https://openalex.org/W2119443761","https://openalex.org/W2122192356","https://openalex.org/W2135305191","https://openalex.org/W2163931868","https://openalex.org/W2233009745","https://openalex.org/W2270000065","https://openalex.org/W2314313576","https://openalex.org/W2412953627","https://openalex.org/W2462002236","https://openalex.org/W2481775463","https://openalex.org/W2520859385","https://openalex.org/W2558085466","https://openalex.org/W2562745862","https://openalex.org/W2604281458","https://openalex.org/W2618372620","https://openalex.org/W2752952648","https://openalex.org/W4295526211"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2356715721","https://openalex.org/W2087757984","https://openalex.org/W2356226573","https://openalex.org/W4245057904","https://openalex.org/W3020506472","https://openalex.org/W2325048728","https://openalex.org/W56905705","https://openalex.org/W2159151868","https://openalex.org/W2067348621"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,13],"the":[4,10,14,33,37,45,49,55,65,71,87,94,97,104,107,118,131,139,144,147,154,162,170,174,179,184,187,191,199,204],"influence":[5],"of":[6,16,36,96,106,112,128,133,146,203,215],"two":[7,62],"scales":[8,63],"in":[9,64,85,117,123,168],"frequency":[11,51,66],"domain":[12,67],"behaviors":[15],"a":[17,22,58,76,81],"typical":[18],"dynamical":[19],"system":[20],"with":[21,40,61,93,165],"double":[23,41],"Hopf":[24,42,209],"bifurcation.":[25],"By":[26],"introducing":[27],"an":[28],"external":[29],"periodic":[30],"excitation":[31],"to":[32,80,161],"normal":[34],"form":[35],"vector":[38],"field":[39],"bifurcation":[43,200],"at":[44,198],"origin":[46],"and":[47,90,143,178,190],"taking":[48],"exciting":[50,73,108],"far":[52],"less":[53],"than":[54],"natural":[56],"frequency,":[57],"theoretical":[59],"model":[60],"is":[68,135,151],"established.":[69],"Regarding":[70],"whole":[72],"term":[74],"as":[75],"slow-varying":[77,98],"parameter":[78,99],"leads":[79],"generalized":[82,119],"autonomous":[83,120],"system,":[84,121],"which":[86,134,169],"equilibrium":[88,148],"branches":[89],"their":[91],"bifurcations":[92,113,145,210],"variation":[95],"can":[100],"be":[101,115],"derived.":[102],"With":[103],"increase":[105],"amplitude,":[109],"different":[110,126,213],"types":[111],"may":[114,159,194,211],"involved":[116],"resulting":[122],"several":[124],"qualitatively":[125],"forms":[127,214],"bursting":[129,163],"attractors,":[130],"mechanism":[132],"presented":[136],"by":[137],"overlapping":[138],"transformed":[140],"phase":[141],"portraits":[142],"branches.":[149],"It":[150],"found":[152],"that":[153],"single":[155,175],"mode":[156,176,181],"2D":[157],"torus":[158],"evolve":[160],"attractors":[164],"mixed":[166,180],"modes,":[167],"trajectory":[171],"alternates":[172],"between":[173,186],"oscillations":[177],"oscillations.":[182,218],"Furthermore,":[183],"transitions":[185],"quiescent":[188],"states":[189,193],"spiking":[192,217],"not":[195],"occur":[196],"exactly":[197],"points":[201],"because":[202],"slow":[205],"passage":[206],"effect,":[207],"while":[208],"cause":[212],"repetitive":[216]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
