{"id":"https://openalex.org/W2104430388","doi":"https://doi.org/10.1137/040615535","title":"A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales","display_name":"A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2104430388","doi":"https://doi.org/10.1137/040615535","mag":"2104430388"},"language":"en","primary_location":{"id":"doi:10.1137/040615535","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040615535","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","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/A5029157201","display_name":"Robert Clewley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Clewley","raw_affiliation_strings":["Boston Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston Univ","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046627918","display_name":"Horacio G. Rotstein","orcid":"https://orcid.org/0000-0002-4387-5160"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Horacio G. Rotstein","raw_affiliation_strings":["Boston Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston Univ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077516931","display_name":"Nancy Kopell","orcid":"https://orcid.org/0000-0002-8568-8750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nancy Kopell","raw_affiliation_strings":["Boston Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston Univ","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0042,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.76427069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"3","first_page":"732","last_page":"759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.998199999332428,"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":0.998199999332428,"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":0.9965000152587891,"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/T10581","display_name":"Neural dynamics and brain function","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8595664501190186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6804588437080383},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6684361100196838},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6636329889297485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6326654553413391},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.5619750618934631},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5025889873504639},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5002255439758301},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4983508586883545},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4951590597629547},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3613213896751404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2614911198616028},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09283870458602905}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8595664501190186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6804588437080383},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6684361100196838},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6636329889297485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6326654553413391},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.5619750618934631},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5025889873504639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5002255439758301},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4983508586883545},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4951590597629547},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3613213896751404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2614911198616028},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09283870458602905},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040615535","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040615535","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.65.4678","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.4678","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wolff.bu.edu/publ/local/ClewleyRotsteinKopell2005.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.1531","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.1531","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wolff.bu.edu/publ/local/ClewleyRRotsteinHGKopellN_AcomputationaltoolforthereductionofnonlinearODEsystemspossessingmultiplescales_2005.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W99189181","https://openalex.org/W155232331","https://openalex.org/W1491439616","https://openalex.org/W1493673410","https://openalex.org/W1501360999","https://openalex.org/W1524412113","https://openalex.org/W1524794587","https://openalex.org/W1561090407","https://openalex.org/W1565264866","https://openalex.org/W1570007728","https://openalex.org/W1571781160","https://openalex.org/W1579475312","https://openalex.org/W1585773866","https://openalex.org/W1594130515","https://openalex.org/W1608340114","https://openalex.org/W1608471504","https://openalex.org/W1677882857","https://openalex.org/W1757730752","https://openalex.org/W1948806673","https://openalex.org/W1964004822","https://openalex.org/W1967848725","https://openalex.org/W1977177901","https://openalex.org/W1978610085","https://openalex.org/W1981538969","https://openalex.org/W1985940938","https://openalex.org/W1989495963","https://openalex.org/W1990323937","https://openalex.org/W1992476998","https://openalex.org/W2003600785","https://openalex.org/W2008000547","https://openalex.org/W2009375605","https://openalex.org/W2011459128","https://openalex.org/W2012747988","https://openalex.org/W2040237110","https://openalex.org/W2041720311","https://openalex.org/W2046424015","https://openalex.org/W2059316647","https://openalex.org/W2059625173","https://openalex.org/W2063576299","https://openalex.org/W2068844879","https://openalex.org/W2069870748","https://openalex.org/W2070660732","https://openalex.org/W2071147887","https://openalex.org/W2074020883","https://openalex.org/W2079481027","https://openalex.org/W2079484715","https://openalex.org/W2081411433","https://openalex.org/W2088678566","https://openalex.org/W2089876099","https://openalex.org/W2089995439","https://openalex.org/W2093749510","https://openalex.org/W2095265457","https://openalex.org/W2101714536","https://openalex.org/W2108311308","https://openalex.org/W2112631723","https://openalex.org/W2134072465","https://openalex.org/W2138278836","https://openalex.org/W2141906015","https://openalex.org/W2142878252","https://openalex.org/W2144067591","https://openalex.org/W2148694408","https://openalex.org/W2149525340","https://openalex.org/W2150936934","https://openalex.org/W2154953441","https://openalex.org/W2157616412","https://openalex.org/W2164761951","https://openalex.org/W2169178475","https://openalex.org/W2476484764","https://openalex.org/W2486576829","https://openalex.org/W2612743911","https://openalex.org/W4210509282","https://openalex.org/W4213388037","https://openalex.org/W4214617048","https://openalex.org/W4230906466","https://openalex.org/W4246342582","https://openalex.org/W4255777804","https://openalex.org/W4292023222"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2377513064","https://openalex.org/W2952544653"],"abstract_inverted_index":{"Near":[0],"an":[1,85,187],"orbit":[2],"of":[3,28,49,54,56,69,78,96,123,145,199,216,253],"interest":[4],"in":[5,51,66,165,175,178,201,208],"a":[6,39,52,94,107,141,239,250,254],"dynamical":[7,67,143],"system,":[8],"it":[9],"is":[10,34,99,104,110,140],"typical":[11],"to":[12,84,133,185,206,223],"ask":[13],"which":[14,246],"variables":[15,117,127],"dominate":[16],"its":[17,24,89],"structure":[18,33,50],"at":[19,152],"what":[20],"times.":[21,155],"What":[22,30],"are":[23,63,128,150],"principal":[25],"local":[26,31],"degrees":[27],"freedom?":[29],"bifurcation":[32],"most":[35],"appropriate?":[36],"We":[37],"introduce":[38],"combined":[40],"numerical":[41,230],"and":[42,168,177,203],"analytical":[43],"technique":[44,75,157],"that":[45,62,81,109,149],"aids":[46],"the":[47,79,114,136,166,193,213,217],"identification":[48],"class":[53],"systems":[55],"nonlinear":[57],"ordinary":[58],"differential":[59],"equations":[60],"(ODEs)":[61],"commonly":[64],"applied":[65],"models":[68,98,148],"physical":[70],"processes.":[71],"This":[72,211],"\"dominant":[73],"scale\"":[74],"prioritizes":[76],"consideration":[77],"influence":[80],"distinguished":[82],"\"inputs\"":[83],"ODE":[86],"have":[87,196,235],"on":[88,161,229,249],"dynamics.":[90],"On":[91],"this":[92],"basis":[93],"sequence":[95],"reduced":[97,146],"derived,":[100],"where":[101],"each":[102],"model":[103],"valid":[105],"for":[106],"duration":[108],"determined":[111],"self-consistently":[112],"as":[113],"system\u2019s":[115],"state":[116,209],"evolve.":[118],"The":[119,138,156],"characteristic":[120],"time":[121,176,202],"scales":[122],"all":[124],"sufficiently":[125],"dominant":[126],"also":[129],"taken":[130],"into":[131,238],"account":[132],"further":[134],"reduce":[135],"model.":[137,259],"result":[139],"hybrid":[142],"system":[144,195,218],"differential-algebraic":[147],"switched":[151],"discrete":[153],"event":[154],"does":[158],"not":[159],"rely":[160],"explicit":[162],"small":[163],"parameters":[164],"ODEs":[167],"automatically":[169],"detects":[170],"changing":[171],"scale":[172],"separation":[173],"both":[174],"\"dominance":[179],"strength\"":[180],"(a":[181],"quantity":[182],"we":[183,247],"derive":[184],"measure":[186],"input\u2019s":[188],"influence).":[189],"Reduced":[190],"regimes":[191],"describing":[192],"full":[194],"quantified":[197],"domains":[198],"validity":[200],"with":[204],"respect":[205],"variation":[207],"variables.":[210],"enables":[212],"qualitative":[214],"analysis":[215],"near":[219],"known":[220],"orbits":[221],"(e.g.,":[222],"study":[224],"bifurcations)":[225],"without":[226],"sole":[227],"reliance":[228],"shooting":[231],"methods.":[232],"These":[233],"methods":[234],"been":[236],"incorporated":[237],"new":[240],"software":[241],"tool":[242],"named":[243],"{\\sc":[244],"Dssrt},":[245],"demonstrate":[248],"limit":[251],"cycle":[252],"synaptically":[255],"driven":[256],"Hodgkin--Huxley":[257],"neuron":[258]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}