{"id":"https://openalex.org/W2602641764","doi":"https://doi.org/10.1109/tac.2017.2688583","title":"Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms","display_name":"Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms","publication_year":2017,"publication_date":"2017-03-31","ids":{"openalex":"https://openalex.org/W2602641764","doi":"https://doi.org/10.1109/tac.2017.2688583","mag":"2602641764"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2688583","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2688583","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5054421000","display_name":"Min Xiao","orcid":"https://orcid.org/0000-0002-8992-153X"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Xiao","raw_affiliation_strings":["College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108050907","display_name":"Wei Xing Zheng","orcid":"https://orcid.org/0000-0002-0572-5938"},"institutions":[{"id":"https://openalex.org/I63525965","display_name":"Western Sydney University","ror":"https://ror.org/03t52dk35","country_code":"AU","type":"education","lineage":["https://openalex.org/I63525965"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Wei Xing Zheng","raw_affiliation_strings":["School of Computing, Western Sydney University, Sydney, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, Western Sydney University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I63525965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005382201","display_name":"Guo\u2010Ping Jiang","orcid":"https://orcid.org/0000-0001-9448-0989"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoping Jiang","raw_affiliation_strings":["College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.5468,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.97029473,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"62","issue":"9","first_page":"4819","last_page":"4826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9983999729156494,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9983999729156494,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9918000102043152,"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6993003487586975},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6845448017120361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6819919943809509},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5914087295532227},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5874677896499634},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5428344011306763},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5019106864929199},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.49238598346710205},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4727005958557129},{"id":"https://openalex.org/keywords/network-congestion","display_name":"Network congestion","score":0.47170090675354004},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3367680311203003},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3119361102581024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2238684594631195},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1046387255191803},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.06441468000411987},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06342029571533203}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6993003487586975},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6845448017120361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6819919943809509},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5914087295532227},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5874677896499634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5428344011306763},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5019106864929199},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.49238598346710205},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4727005958557129},{"id":"https://openalex.org/C195563490","wikidata":"https://www.wikidata.org/wiki/Q180368","display_name":"Network congestion","level":3,"score":0.47170090675354004},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3367680311203003},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3119361102581024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2238684594631195},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1046387255191803},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.06441468000411987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06342029571533203},{"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2017.2688583","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2688583","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1095396022","display_name":null,"funder_award_id":"61573194","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1268832336","display_name":"Quantized identification of feedback control systems","funder_award_id":"DP120104986","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G4794703675","display_name":null,"funder_award_id":"61374180","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8228501484","display_name":null,"funder_award_id":"61573096","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W56786142","https://openalex.org/W148919764","https://openalex.org/W1509146820","https://openalex.org/W1516580706","https://openalex.org/W1572996156","https://openalex.org/W1968134101","https://openalex.org/W1969313263","https://openalex.org/W1971609228","https://openalex.org/W1990830194","https://openalex.org/W2000666669","https://openalex.org/W2008052025","https://openalex.org/W2011839804","https://openalex.org/W2012724484","https://openalex.org/W2012748134","https://openalex.org/W2013235495","https://openalex.org/W2033470589","https://openalex.org/W2038840346","https://openalex.org/W2047887072","https://openalex.org/W2050580331","https://openalex.org/W2051483432","https://openalex.org/W2053497389","https://openalex.org/W2053507305","https://openalex.org/W2054089616","https://openalex.org/W2057601201","https://openalex.org/W2074823107","https://openalex.org/W2075110582","https://openalex.org/W2075664962","https://openalex.org/W2079894097","https://openalex.org/W2088101241","https://openalex.org/W2106393665","https://openalex.org/W2111025408","https://openalex.org/W2120827882","https://openalex.org/W2123191569","https://openalex.org/W2136254520","https://openalex.org/W2142325999","https://openalex.org/W2148445149","https://openalex.org/W2151015649","https://openalex.org/W2155306171","https://openalex.org/W2168670619","https://openalex.org/W2294239831","https://openalex.org/W2343743814","https://openalex.org/W2595737758","https://openalex.org/W2787959293","https://openalex.org/W4253062931","https://openalex.org/W4296180618","https://openalex.org/W6602327797","https://openalex.org/W6630828063"],"related_works":["https://openalex.org/W2317351040","https://openalex.org/W4309781665","https://openalex.org/W2052299349","https://openalex.org/W4285447065","https://openalex.org/W1988622314","https://openalex.org/W1901944325","https://openalex.org/W2393949104","https://openalex.org/W3046201198","https://openalex.org/W2789801754","https://openalex.org/W4293061921"],"abstract_inverted_index":{"In":[0,14],"this":[1,85],"technical":[2],"note,":[3],"fractional-order":[4,36,59,76],"congestion":[5,21,80],"control":[6,22,26,81],"systems":[7,57],"are":[8,28,52,64,92,109],"introduced":[9],"for":[10,46,73],"the":[11,17,24,47,68,74,88,105,114],"first":[12],"time.":[13],"comparison":[15],"with":[16],"conventional":[18],"integer-order":[19,55],"dual":[20,79],"algorithms,":[23],"fractional":[25],"algorithms":[27,82],"more":[29],"accurate":[30],"and":[31,98],"versatile.":[32],"Bifurcation":[33],"theory":[34],"in":[35,84],"differential":[37],"equations":[38],"is":[39],"still":[40],"an":[41],"outstanding":[42],"problem.":[43],"Sufficient":[44],"conditions":[45,63],"occurrence":[48],"of":[49,70,78,90,101],"Hopf":[50,71,95],"bifurcations":[51,72,91,96],"extended":[53],"from":[54,104],"dynamical":[56],"to":[58,66,112],"cases.":[60],"Then,":[61],"these":[62],"used":[65],"establish":[67],"existence":[69],"delayed":[75],"model":[77],"proposed":[83],"note.":[86],"Finally,":[87],"onsets":[89],"identified,":[93],"where":[94],"occur":[97],"a":[99],"family":[100],"oscillations":[102],"bifurcate":[103],"equilibrium.":[106],"Illustrative":[107],"examples":[108],"also":[110],"provided":[111],"demonstrate":[113],"theoretical":[115],"results.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}