{"id":"https://openalex.org/W2782469032","doi":"https://doi.org/10.1142/s0218127417502029","title":"Bifurcation Regulations Governed by Delay Self-Control Feedback in a Stochastic Birhythmic System","display_name":"Bifurcation Regulations Governed by Delay Self-Control Feedback in a Stochastic Birhythmic System","publication_year":2017,"publication_date":"2017-12-15","ids":{"openalex":"https://openalex.org/W2782469032","doi":"https://doi.org/10.1142/s0218127417502029","mag":"2782469032"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417502029","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502029","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/A5022767545","display_name":"Zhidan Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhidan Ma","raw_affiliation_strings":["School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039565337","display_name":"Lijuan Ning","orcid":"https://orcid.org/0000-0003-1456-5806"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijuan Ning","raw_affiliation_strings":["School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710119, P. R. China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022767545"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":0.8602,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73705265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"13","first_page":"1750202","last_page":"1750202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","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/T11513","display_name":"stochastic dynamics and bifurcation","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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9987999796867371,"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":0.9973000288009644,"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/control-theory","display_name":"Control theory (sociology)","score":0.6890676021575928},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6063525676727295},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5761886835098267},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5752585530281067},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5033487677574158},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.4755032956600189},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4708261787891388},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4370180666446686},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4314066171646118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4032588303089142},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3583734631538391},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3278501033782959},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.27841541171073914},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2721465826034546},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22573566436767578},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18372786045074463},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08199161291122437},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07855728268623352}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6890676021575928},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6063525676727295},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5761886835098267},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5752585530281067},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5033487677574158},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.4755032956600189},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4708261787891388},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4370180666446686},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4314066171646118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4032588303089142},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3583734631538391},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3278501033782959},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.27841541171073914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2721465826034546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22573566436767578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18372786045074463},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08199161291122437},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07855728268623352},{"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417502029","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502029","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/G8606496008","display_name":null,"funder_award_id":"11202120","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1454351668","https://openalex.org/W1660308075","https://openalex.org/W1978820760","https://openalex.org/W1978830021","https://openalex.org/W1992069309","https://openalex.org/W1995353004","https://openalex.org/W2006858638","https://openalex.org/W2007287229","https://openalex.org/W2013096807","https://openalex.org/W2014939413","https://openalex.org/W2019882646","https://openalex.org/W2026787390","https://openalex.org/W2033866819","https://openalex.org/W2034962833","https://openalex.org/W2035665802","https://openalex.org/W2037505299","https://openalex.org/W2037541444","https://openalex.org/W2043486667","https://openalex.org/W2056170808","https://openalex.org/W2063867371","https://openalex.org/W2068551947","https://openalex.org/W2074157282","https://openalex.org/W2076337319","https://openalex.org/W2083117595","https://openalex.org/W2092889223","https://openalex.org/W2112125796","https://openalex.org/W2119909362","https://openalex.org/W2170366731","https://openalex.org/W2208711953","https://openalex.org/W2339204715","https://openalex.org/W2472788249","https://openalex.org/W2532940938","https://openalex.org/W3103815826","https://openalex.org/W6600788769"],"related_works":["https://openalex.org/W3176128920","https://openalex.org/W3160507409","https://openalex.org/W2018197389","https://openalex.org/W1483322194","https://openalex.org/W2555766691","https://openalex.org/W2389191465","https://openalex.org/W2262919813","https://openalex.org/W2093031412","https://openalex.org/W2392185587","https://openalex.org/W2356049208"],"abstract_inverted_index":{"We":[0],"aim":[1],"to":[2,16,26,32,123],"investigate":[3],"bifurcation":[4,73],"behaviors":[5],"in":[6],"a":[7],"stochastic":[8,53],"birhythmic":[9],"van":[10],"der":[11],"Pol":[12],"(BVDP)":[13],"system":[14],"subjected":[15],"delay":[17,29,63,86],"self-control":[18,30,64],"feedback.":[19],"First,":[20],"the":[21,28,60,81,89,96,102,108,116,126,138],"harmonic":[22],"approximation":[23],"is":[24,78,119],"adopted":[25],"drive":[27],"feedback":[31,65,83],"state":[33],"variables":[34],"without":[35],"delay.":[36],"Then,":[37],"Fokker\u2013Planck\u2013Kolmogorov":[38],"(FPK)":[39],"equation":[40],"and":[41,85],"stationary":[42],"probability":[43],"density":[44],"function":[45],"(SPDF)":[46],"for":[47],"amplitude":[48,91,104],"are":[49,75,112],"obtained":[50],"by":[51,133],"applying":[52],"averaging":[54],"method.":[55],"Finally,":[56],"dynamical":[57],"scenarios":[58],"of":[59,62,128,137],"change":[61],"as":[66,68],"well":[67],"noise":[69,99],"that":[70],"markedly":[71],"influence":[72],"performance":[74],"observed.":[76],"It":[77],"found":[79],"that:":[80],"big":[82,98],"strength":[84,100],"will":[87],"suppress":[88],"large":[90,103],"limit":[92],"cycle":[93],"(LC)":[94],"while":[95],"relatively":[97],"facilitates":[101],"LC,":[105],"which":[106],"imply":[107],"proposed":[109],"regulation":[110],"strategies":[111],"feasible.":[113],"Interestingly":[114],"enough,":[115],"inner":[117],"LC":[118],"never":[120],"destroyed":[121],"due":[122],"noise.":[124],"Furthermore,":[125],"validity":[127],"analytical":[129],"results":[130],"was":[131],"verified":[132],"Monte":[134],"Carlo":[135],"simulation":[136],"dynamics.":[139]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}