{"id":"https://openalex.org/W2086154017","doi":"https://doi.org/10.1142/s0218127404011235","title":"BIFURCATIONS IN APPROXIMATE SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS","display_name":"BIFURCATIONS IN APPROXIMATE SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W2086154017","doi":"https://doi.org/10.1142/s0218127404011235","mag":"2086154017"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127404011235","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011235","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/A5078620782","display_name":"Christopher Baker","orcid":"https://orcid.org/0000-0003-3899-7080"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"CHRISTOPHER T. H. BAKER","raw_affiliation_strings":["Department of Mathematics, The University of Manchester, Manchester, M13 9PL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Manchester, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103493024","display_name":"Judith M. Ford","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"JUDITH M. FORD","raw_affiliation_strings":["Department of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, UK","Department of Mathematics, UMIST, P.O. BOX 88, Manchester, M60 1QD, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Mathematics, UMIST, P.O. BOX 88, Manchester, M60 1QD, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087725371","display_name":"Neville J. Ford","orcid":"https://orcid.org/0000-0002-9446-437X"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"NEVILLE J. FORD","raw_affiliation_strings":["Department of Mathematics, University College Chester, Parkgate Road, Chester, CH1 4BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College Chester, Parkgate Road, Chester, CH1 4BJ, UK","institution_ids":["https://openalex.org/I137265193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7099,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84345258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"14","issue":"09","first_page":"2999","last_page":"3021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6739274263381958},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6561800837516785},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.6428368091583252},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.5204085111618042},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4833962023258209},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4768748879432678},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4743027687072754},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4411281943321228},{"id":"https://openalex.org/keywords/wiener-process","display_name":"Wiener process","score":0.4249497652053833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35431069135665894},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21359848976135254}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6739274263381958},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6561800837516785},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.6428368091583252},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.5204085111618042},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4833962023258209},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4768748879432678},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4743027687072754},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4411281943321228},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.4249497652053833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35431069135665894},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21359848976135254},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127404011235","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127404011235","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"},{"id":"pmh:oai:chesterrep.openrepository.com:10034/68535","is_oa":false,"landing_page_url":"http://hdl.handle.net/10034/68535","pdf_url":null,"source":{"id":"https://openalex.org/S4377196415","display_name":"ChesterRep (University of Chester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I137265193","host_organization_name":"University of Chester","host_organization_lineage":["https://openalex.org/I137265193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W66872489","https://openalex.org/W305513724","https://openalex.org/W1275718198","https://openalex.org/W1550341792","https://openalex.org/W1990442324","https://openalex.org/W1998379200","https://openalex.org/W2012478756","https://openalex.org/W2019317114","https://openalex.org/W2047017331","https://openalex.org/W2048017269","https://openalex.org/W2048020646","https://openalex.org/W2048677413","https://openalex.org/W2063687827","https://openalex.org/W2067450357","https://openalex.org/W2067576443","https://openalex.org/W2081188152","https://openalex.org/W2081827062","https://openalex.org/W2082256594","https://openalex.org/W2095172584","https://openalex.org/W2131189822","https://openalex.org/W2143938206","https://openalex.org/W2145137020","https://openalex.org/W2467963231","https://openalex.org/W2484713419","https://openalex.org/W2977318642","https://openalex.org/W4210417410","https://openalex.org/W4210960242","https://openalex.org/W4211202937","https://openalex.org/W4245357092","https://openalex.org/W4293510232"],"related_works":["https://openalex.org/W2014550429","https://openalex.org/W2088712741","https://openalex.org/W2954344910","https://openalex.org/W3033385751","https://openalex.org/W2037491434","https://openalex.org/W4321795738","https://openalex.org/W2952903495","https://openalex.org/W2035506987","https://openalex.org/W2007809188","https://openalex.org/W2387215919"],"abstract_inverted_index":{"We":[0,40,156,202],"consider":[1],"stochastic":[2,131,141,154,176],"delay":[3,66,177],"differential":[4,67,178],"equations":[5,200],"of":[6,52,54,76,93,99,105,114,129,137,152,161,167,189,210],"the":[7,14,35,49,63,91,94,100,112,130,140,149,153,159,168,190,195,199,214],"form":[8],"[Formula:":[9],"see":[10],"text]":[11],"interpreted":[12],"in":[13,43,48,90,175,213],"It\u00f4":[15],"sense,":[16],"with":[17],"Y(t)=\u03a6(t)":[18],"for":[19,69,139,185,198],"t\u2208[t":[20],"0":[21,23],"-\u03c4,t":[22],"]":[24],"(here,":[25],"W(t)":[26],"is":[27,34,72],"a":[28,73,208],"standard":[29],"Wiener":[30],"process":[31],"and":[32,57,79,96,125,143],"\u03c4>0":[33],"constant":[36],"\"lag\",":[37],"or":[38],"\"time-lag\").":[39],"are":[41,108,145],"interested":[42],"bifurcations":[44,174],"(that":[45],"is,":[46],"changes":[47,88],"qualitative":[50],"behavior":[51,92],"solutions":[53,98],"these":[55],"equations)":[56],"we":[58,119],"draw":[59],"on":[60],"insights":[61],"from":[62],"related":[64],"deterministic":[65,123],"equation,":[68],"which":[70],"there":[71],"substantial":[74],"body":[75],"known":[77],"theory,":[78],"numerical":[80,162],"results":[81,124,160],"that":[82,133,164,170],"enable":[83],"us":[84],"to":[85,110,147,207],"discuss":[86],"where":[87],"occur":[89],"(exact":[95],"approximate)":[97],"equation.":[101],"Rather":[102],"diverse":[103],"components":[104],"mathematical":[106],"background":[107],"necessary":[109],"understand":[111],"questions":[113,212],"interest.":[115],"In":[116],"this":[117],"paper":[118],"first":[120],"review":[121],"some":[122,126,166],"basic":[127],"elements":[128],"analysis":[132],"(i)":[134],"suggests":[135],"lines":[136],"investigation":[138,151],"case":[142],"(ii)":[144],"expected":[146],"facilitate":[148],"theoretical":[150],"problem.":[155],"then":[157],"present":[158],"experiments":[163],"illustrate":[165],"complexities":[169],"arise":[171],"when":[172],"considering":[173],"equations.":[179],"They":[180],"give":[181],"prima":[182],"facie":[183],"evidence":[184],"certain":[186],"convergence":[187],"properties":[188],"bifurcation":[191],"points":[192],"estimated":[193],"using":[194],"Euler\u2013Maruyama":[196],"method":[197],"considered.":[201],"conclude":[203],"by":[204],"drawing":[205],"attention":[206],"number":[209],"open":[211],"field.":[215]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}