{"id":"https://openalex.org/W2065859134","doi":"https://doi.org/10.1137/080725283","title":"Periodic Solutions and the Global Attractor in a System of Delay Differential Equations","display_name":"Periodic Solutions and the Global Attractor in a System of Delay Differential Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2065859134","doi":"https://doi.org/10.1137/080725283","mag":"2065859134"},"language":"en","primary_location":{"id":"doi:10.1137/080725283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080725283","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_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 Mathematical Analysis","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/A5039956150","display_name":"Taishan Yi","orcid":"https://orcid.org/0000-0002-5028-5492"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Taishan Yi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100384017","display_name":"Yuming Chen","orcid":"https://orcid.org/0000-0002-9841-0504"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuming Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100599435","display_name":"Jian Wu","orcid":"https://orcid.org/0000-0002-3394-1507"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianhong Wu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039956150"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.613,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.93008931,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"1","first_page":"24","last_page":"63"},"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":0.9987999796867371,"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":0.9987999796867371,"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":0.998199999332428,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8310974836349487},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7660199403762817},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7249299883842468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6085008978843689},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5766730308532715},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5021367073059082},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.45520973205566406},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4117279350757599},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12141656875610352},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08784621953964233}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8310974836349487},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7660199403762817},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7249299883842468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6085008978843689},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5766730308532715},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5021367073059082},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.45520973205566406},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4117279350757599},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12141656875610352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08784621953964233},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080725283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080725283","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_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 Mathematical Analysis","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":15,"referenced_works":["https://openalex.org/W88348005","https://openalex.org/W1552317631","https://openalex.org/W1964053068","https://openalex.org/W1980029699","https://openalex.org/W1980921643","https://openalex.org/W1999606590","https://openalex.org/W2006188446","https://openalex.org/W2020174839","https://openalex.org/W2038696548","https://openalex.org/W2057059553","https://openalex.org/W2065450947","https://openalex.org/W2071267744","https://openalex.org/W2076727539","https://openalex.org/W2112246162","https://openalex.org/W2128084896"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2030956422"],"abstract_inverted_index":{"We":[0,17,44],"consider":[1],"a":[2,9,40,63],"system":[3,64],"of":[4,28,39,61,68,72],"delay":[5],"differential":[6],"equations":[7],"with":[8,31],"delayed":[10],"excitatory":[11],"feedback":[12],"loop":[13],"and":[14,22,26,53,75],"instantaneous":[15],"damping.":[16],"develop":[18],"the":[19,24,37,47,58,66,69],"Cao\u2013Krisztin\u2013Walther":[20],"technique":[21],"establish":[23],"existence":[25],"uniqueness":[27],"periodic":[29,76],"solutions":[30],"prescribed":[32],"oscillation":[33],"frequencies":[34],"(characterized":[35],"by":[36],"values":[38],"discrete":[41],"Lyapunov":[42],"functional).":[43],"then":[45],"use":[46],"Poincar\u00e9-Bendixson":[48],"theorem":[49],"due":[50],"to":[51,55],"Mallet-Paret":[52],"Sell":[54],"show":[56],"that":[57],"global":[59],"attractor":[60],"such":[62],"is":[65],"union":[67],"unstable":[70],"sets":[71],"stationary":[73],"points":[74],"orbits.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}