{"id":"https://openalex.org/W1966488387","doi":"https://doi.org/10.1137/s0036141001388592","title":"Memory Driven Instability in a Diffusion Process","display_name":"Memory Driven Instability in a Diffusion Process","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1966488387","doi":"https://doi.org/10.1137/s0036141001388592","mag":"1966488387"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001388592","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5024547678","display_name":"B. R. Duffy","orcid":"https://orcid.org/0000-0003-2687-7938"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brian R. Duffy","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006030760","display_name":"Pedro Freitas","orcid":"https://orcid.org/0000-0002-2007-5259"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pedro Freitas","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071213403","display_name":"Michael Grinfeld","orcid":"https://orcid.org/0000-0002-3897-8819"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Grinfeld","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.732,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":29,"citation_normalized_percentile":{"value":0.937368,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"33","issue":"5","first_page":"1090","last_page":"1106"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9996,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9996,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9971,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9886,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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-bifurcation","display_name":"Homoclinic bifurcation","score":0.4791931},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.43549097},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.41116446}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8360557},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.65481067},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.63365954},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.57117665},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5551715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5516025},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4995618},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.49671394},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.4791931},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.43549097},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.41116446},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15400296},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.12022486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11325428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08398035},{"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/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001388592","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":19,"referenced_works":["https://openalex.org/W1547666981","https://openalex.org/W1557040331","https://openalex.org/W1561704653","https://openalex.org/W1975390908","https://openalex.org/W1976489357","https://openalex.org/W1982357817","https://openalex.org/W2004406097","https://openalex.org/W2012210227","https://openalex.org/W2038991247","https://openalex.org/W2054563910","https://openalex.org/W2063415057","https://openalex.org/W2079970514","https://openalex.org/W2089876099","https://openalex.org/W2122345489","https://openalex.org/W2136944745","https://openalex.org/W2462517821","https://openalex.org/W3103942046","https://openalex.org/W4213264637","https://openalex.org/W4298313869"],"related_works":["https://openalex.org/W944345475","https://openalex.org/W352136236","https://openalex.org/W3115184012","https://openalex.org/W2890492950","https://openalex.org/W2356323067","https://openalex.org/W2045215015","https://openalex.org/W2042800579","https://openalex.org/W2010606039","https://openalex.org/W1999123830","https://openalex.org/W1547807244"],"abstract_inverted_index":{"We":[0,33,74],"consider":[1],"the":[2,22,29,35,45,67,71,77,93,101,120],"ndimensional":[3],"version":[4],"of":[5,24,31,37,47,59,66,81,92,110],"a":[6,25,38,48,56,63,105,125],"model":[7],"proposed":[8],"by":[9,103,118],"Olmstead":[10],"et":[11],"al.":[12],"[SIAM":[13],"J.":[14],"Appl.":[15],"Math.,":[16],"46":[17],"(1986),":[18],"pp.":[19],"171--188]":[20],"for":[21,44,89],"flow":[23,102],"non-Newtonian":[26],"fluid":[27],"in":[28,62,70,85],"presence":[30],"memory.":[32],"prove":[34,87],"existence":[36,46,109],"global":[39],"attractor":[40,61],"and":[41,79,112],"obtain":[42],"conditions":[43],"Lyapunov":[49],"functional,":[50],"which":[51],"allows":[52],"us":[53],"to":[54,99],"give":[55],"full":[57],"description":[58],"this":[60],"certain":[64,90],"region":[65],"parameter":[68],"space":[69],"bistable":[72],"case.":[73],"then":[75],"study":[76],"stability":[78],"bifurcation":[80],"stationary":[82],"solutions":[83],"and,":[84],"particular,":[86],"that":[88],"values":[91],"parameters":[94],"it":[95],"is":[96,115],"not":[97],"possible":[98],"stabilize":[100],"increasing":[104],"Rayleigh-type":[106],"number.":[107],"The":[108],"periodic":[111],"homoclinic":[113],"orbits":[114],"also":[116],"shown":[117],"studying":[119],"Bogdanov--Takens":[121],"singularity":[122],"obtained":[123],"from":[124],"center":[126],"manifold":[127],"reduction.":[128]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1966488387","counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-03-18T13:35:31.014571","created_date":"2016-06-24"}