{"id":"https://openalex.org/W2952043395","doi":"https://doi.org/10.1137/14097183x","title":"Classification of Coupled Dynamical Systems with Multiple Delays: Finding the Minimal Number of Delays","display_name":"Classification of Coupled Dynamical Systems with Multiple Delays: Finding the Minimal Number of Delays","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2952043395","doi":"https://doi.org/10.1137/14097183x","mag":"2952043395"},"language":"en","primary_location":{"id":"doi:10.1137/14097183x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14097183x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1301.2051","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025018954","display_name":"Leonhard L\u00fccken","orcid":"https://orcid.org/0000-0001-6103-6531"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"L. L\u00fccken","raw_affiliation_strings":["Weierstrass Institute [Berlin]"],"affiliations":[{"raw_affiliation_string":"Weierstrass Institute [Berlin]","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052919780","display_name":"Jan Philipp Pade","orcid":null},"institutions":[{"id":"https://openalex.org/I4210144795","display_name":"Institut F\u00fcr Angewandte Kulturforschung","ror":"https://ror.org/04dmgcf89","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I4210144795"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. P. Pade","raw_affiliation_strings":["Institut fur Informatik"],"affiliations":[{"raw_affiliation_string":"Institut fur Informatik","institution_ids":["https://openalex.org/I4210144795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057566451","display_name":"Kolja Knauer","orcid":"https://orcid.org/0000-0002-8151-2184"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Knauer","raw_affiliation_strings":["Algorithmes, Graphes et Combinatoire"],"affiliations":[{"raw_affiliation_string":"Algorithmes, Graphes et Combinatoire","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025018954"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":1.7492,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87718803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"1","first_page":"286","last_page":"304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9997000098228455,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9968000054359436,"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/attractor","display_name":"Attractor","score":0.7521190643310547},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6781423091888428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.659837007522583},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5834824442863464},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.501417875289917},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.48114240169525146},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.46888941526412964},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4551647901535034},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4516354203224182},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4454249441623688},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42421025037765503},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.41740691661834717},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41117990016937256},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3874225616455078},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3175618350505829},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30699819326400757},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29834622144699097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28791093826293945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2045837640762329},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13250413537025452}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7521190643310547},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6781423091888428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.659837007522583},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5834824442863464},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.501417875289917},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.48114240169525146},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.46888941526412964},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4551647901535034},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4516354203224182},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4454249441623688},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42421025037765503},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.41740691661834717},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41117990016937256},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3874225616455078},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3175618350505829},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30699819326400757},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29834622144699097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28791093826293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2045837640762329},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13250413537025452},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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":5,"locations":[{"id":"doi:10.1137/14097183x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14097183x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1301.2051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.2051","pdf_url":"https://arxiv.org/pdf/1301.2051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:doi:10.20347/wias.preprint.2067","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00002169","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"preprint"},{"id":"pmh:oai:HAL:hal-01457962v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01457962","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 2015, 14 (1), pp.286-304. ⟨10.1137/14097183X⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:lirmm-01348844v1","is_oa":false,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-01348844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1536-0040","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1301.2051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.2051","pdf_url":"https://arxiv.org/pdf/1301.2051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W359361325","https://openalex.org/W590413840","https://openalex.org/W1586658033","https://openalex.org/W1607633954","https://openalex.org/W1964053068","https://openalex.org/W1965680834","https://openalex.org/W1968187292","https://openalex.org/W1972778382","https://openalex.org/W1976351814","https://openalex.org/W1983171862","https://openalex.org/W1983651206","https://openalex.org/W1983752193","https://openalex.org/W1998046420","https://openalex.org/W2013623261","https://openalex.org/W2014172170","https://openalex.org/W2018903956","https://openalex.org/W2039070048","https://openalex.org/W2043607790","https://openalex.org/W2049929575","https://openalex.org/W2050514524","https://openalex.org/W2055606008","https://openalex.org/W2060813275","https://openalex.org/W2064965260","https://openalex.org/W2074178424","https://openalex.org/W2083535949","https://openalex.org/W2084820442","https://openalex.org/W2088555683","https://openalex.org/W2090387128","https://openalex.org/W2094631910","https://openalex.org/W2099140812","https://openalex.org/W2104454795","https://openalex.org/W2111637466","https://openalex.org/W2114228460","https://openalex.org/W2120026810","https://openalex.org/W2123168499","https://openalex.org/W2123658935","https://openalex.org/W2129091841","https://openalex.org/W2152502378","https://openalex.org/W2258199913","https://openalex.org/W2625711953","https://openalex.org/W2798588639","https://openalex.org/W3101572482","https://openalex.org/W3103879811","https://openalex.org/W3105740435","https://openalex.org/W4211202937","https://openalex.org/W4255306344","https://openalex.org/W4301046466"],"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/W2460935991","https://openalex.org/W2377513064"],"abstract_inverted_index":{"In":[0,75],"this":[1,44,50,100],"article":[2],"we":[3,52,77,103],"study":[4],"networks":[5,16],"of":[6,42,72,83,88,95,123,134,144,149],"coupled":[7],"dynamical":[8,32],"systems":[9,63],"with":[10],"time-delayed":[11],"connections.":[12],"If":[13],"two":[14],"such":[15],"hold":[17],"different":[18,31,70,124],"delays":[19,43,125,150],"on":[20],"the":[21,47,86,93,113,121,130,135,141,145],"connections":[22],"it":[23,156],"is":[24,45,97,110,126,151],"in":[25,119,152],"general":[26,153],"possible":[27],"that":[28,38,92,105,140],"they":[29],"exhibit":[30],"behavior":[33],"as":[34],"well.":[35],"We":[36,138],"prove":[37],"for":[39,79],"particular":[40],"sets":[41,71],"not":[46,127],"case.":[48],"To":[49],"aim":[51],"introduce":[53],"a":[54,80,116],"componentwise":[55],"timeshift":[56],"transformation":[57],"(CTT)":[58],"which":[59,64,109,120],"allows":[60],"to":[61],"classify":[62],"possess":[65],"equivalent":[66],"dynamics,":[67],"though":[68],"possibly":[69],"connection":[73],"delays.":[74],"particular,":[76],"show":[78,104],"large":[81],"class":[82,108],"semiflows":[84],"(including":[85],"case":[87],"delay":[89],"differential":[90],"equations)":[91],"stability":[94],"attractors":[96],"invariant":[98],"under":[99],"transformation.":[101],"Moreover":[102],"each":[106],"equivalence":[107],"mediated":[111],"by":[112],"CTT":[114],"possesses":[115],"representative":[117],"system":[118],"number":[122],"larger":[128],"than":[129,155],"cycle":[131],"space":[132,148],"dimension":[133,143],"underlying":[136],"graph.":[137],"conclude":[139],"'true'":[142],"corresponding":[146],"parameter":[147],"smaller":[154],"appears":[157],"at":[158],"first":[159],"glance.":[160]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2019-06-27T00:00:00"}