{"id":"https://openalex.org/W1974961965","doi":"https://doi.org/10.1137/s0036139997325679","title":"Averaging Theory for Delay Difference Equations with Time-Varying Delays","display_name":"Averaging Theory for Delay Difference Equations with Time-Varying Delays","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1974961965","doi":"https://doi.org/10.1137/s0036139997325679","mag":"1974961965"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139997325679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997325679","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":"SIAM Journal on Applied Mathematics","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/A5040451293","display_name":"Brad Lehman","orcid":"https://orcid.org/0000-0003-1120-399X"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brad Lehman","raw_affiliation_strings":["northeastern Univ"],"affiliations":[{"raw_affiliation_string":"northeastern Univ","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010562356","display_name":"S. Weibel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven P. Weibel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040451293"],"corresponding_institution_ids":["https://openalex.org/I12912129"],"apc_list":null,"apc_paid":null,"fwci":0.7781,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.71919741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"4","first_page":"1487","last_page":"1506"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9980999827384949,"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":0.9980999827384949,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9835000038146973,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9714000225067139,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.6570664644241333},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6233835816383362},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.6001718640327454},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.5512363910675049},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4750511646270752},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44689446687698364},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.43621626496315},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37548550963401794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22872599959373474},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09688419103622437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6570664644241333},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6233835816383362},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.6001718640327454},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.5512363910675049},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4750511646270752},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44689446687698364},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.43621626496315},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37548550963401794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22872599959373474},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09688419103622437},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139997325679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997325679","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W146778183","https://openalex.org/W1481616730","https://openalex.org/W1968234937","https://openalex.org/W1983133432","https://openalex.org/W2113921313","https://openalex.org/W2114570773","https://openalex.org/W2326418943","https://openalex.org/W2895674046","https://openalex.org/W3041070869","https://openalex.org/W4252265388"],"related_works":["https://openalex.org/W2373038869","https://openalex.org/W2375908649","https://openalex.org/W2898732673","https://openalex.org/W2614837930","https://openalex.org/W165228748","https://openalex.org/W2410053581","https://openalex.org/W1991810297","https://openalex.org/W2032253950","https://openalex.org/W2131542607","https://openalex.org/W2101148463"],"abstract_inverted_index":{"Although":[0],"the":[1,24,67,76],"theory":[2,41],"of":[3,11,23,26,42,61,70,78],"averaging":[4,43],"has":[5,15],"long":[6],"been":[7],"a":[8,40,71],"classical":[9],"component":[10],"applied":[12,65],"mathematics,":[13],"it":[14],"found":[16],"new":[17],"importance":[18],"in":[19,75],"controls":[20],"engineering":[21],"because":[22],"development":[25],"adaptive":[27,29,68],"identification,":[28],"control,":[30],"and":[31,47],"open-loop":[32],"oscillatory":[33],"control.":[34],"In":[35],"this":[36,62],"paper,":[37],"we":[38],"develop":[39],"on":[44],"both":[45],"finite":[46],"infinite":[48],"time":[49],"intervals":[50],"for":[51],"delay":[52],"difference":[53],"equations":[54],"with":[55],"time-varying":[56,79],"delays.":[57,81],"The":[58],"main":[59],"results":[60],"paper":[63],"are":[64],"to":[66],"identification":[69],"pipe":[72],"mixing":[73],"problem":[74],"presence":[77],"transport":[80]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}