{"id":"https://openalex.org/W4392742999","doi":"https://doi.org/10.1142/s0218127424500251","title":"Stability, Bifurcation and Dynamics in a Network with Delays","display_name":"Stability, Bifurcation and Dynamics in a Network with Delays","publication_year":2024,"publication_date":"2024-02-01","ids":{"openalex":"https://openalex.org/W4392742999","doi":"https://doi.org/10.1142/s0218127424500251"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127424500251","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424500251","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5100340402","display_name":"Xu Xu","orcid":"https://orcid.org/0000-0002-0691-8248"},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xu Xu","raw_affiliation_strings":["College of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-0691-8248","affiliations":[{"raw_affiliation_string":"College of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, P. R. China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103000374","display_name":"Jianming Liu","orcid":"https://orcid.org/0009-0003-5830-8737"},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianming Liu","raw_affiliation_strings":["College of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, P. R. China"],"raw_orcid":"https://orcid.org/0009-0003-5830-8737","affiliations":[{"raw_affiliation_string":"College of Mathematics, Jilin University, 2699 Qianjin Street, Changchun 130012, P. R. China","institution_ids":["https://openalex.org/I194450716"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100340402"],"corresponding_institution_ids":["https://openalex.org/I194450716"],"apc_list":null,"apc_paid":null,"fwci":0.8523,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7214118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"34","issue":"02","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991999864578247,"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":0.9991999864578247,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9990000128746033,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6637227535247803},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6277682781219482},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5967980623245239},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5772958993911743},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5681079030036926},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5446256399154663},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.5087257027626038},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4538983702659607},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4401710331439972},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44001075625419617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.363760769367218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3600934147834778},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2697131335735321},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19111526012420654},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14992058277130127},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08698669075965881}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6637227535247803},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6277682781219482},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5967980623245239},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5772958993911743},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5681079030036926},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5446256399154663},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.5087257027626038},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4538983702659607},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4401710331439972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44001075625419617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.363760769367218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3600934147834778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2697131335735321},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19111526012420654},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14992058277130127},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08698669075965881},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127424500251","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127424500251","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5099999904632568,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G6726359699","display_name":null,"funder_award_id":"12072128","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W171450560","https://openalex.org/W1531715726","https://openalex.org/W1821202608","https://openalex.org/W1945601895","https://openalex.org/W1969361150","https://openalex.org/W2008620264","https://openalex.org/W2036307314","https://openalex.org/W2038197536","https://openalex.org/W2053046489","https://openalex.org/W2064775961","https://openalex.org/W2065029123","https://openalex.org/W2075489015","https://openalex.org/W2079871064","https://openalex.org/W2112090702","https://openalex.org/W2316853122","https://openalex.org/W2528533647","https://openalex.org/W2532867680","https://openalex.org/W2569068769","https://openalex.org/W2744740356","https://openalex.org/W2765706868","https://openalex.org/W2782153856","https://openalex.org/W2790221363","https://openalex.org/W2885804390","https://openalex.org/W2902337500","https://openalex.org/W2920010818","https://openalex.org/W2987171219","https://openalex.org/W2999882870","https://openalex.org/W4254962106"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2923981205","https://openalex.org/W3113797113","https://openalex.org/W2775656422","https://openalex.org/W2054075447","https://openalex.org/W2080238758","https://openalex.org/W2387129305","https://openalex.org/W2923145936","https://openalex.org/W2785329944","https://openalex.org/W3146050852"],"abstract_inverted_index":{"In":[0,127],"real-world":[1],"networks,":[2],"due":[3],"to":[4,119,149],"complex":[5,37,121,173],"topological":[6],"structures":[7],"and":[8,19,36,53,66,90,104,110,143,158],"uncertainties":[9],"such":[10],"as":[11],"time":[12,105],"delays,":[13],"uncontrolled":[14],"systems":[15],"may":[16],"generate":[17,166],"instability":[18],"complexity,":[20],"thereby":[21],"degrading":[22],"network":[23,102],"performance.":[24],"This":[25],"paper":[26],"provides":[27],"a":[28,40],"detailed":[29],"analysis":[30],"of":[31,39,59,62,69,76,100,139,172],"the":[32,49,57,60,63,67,81,98,101,108,120,129,155,169],"stability,":[33],"Hopf":[34,54,70,111],"bifurcation,":[35],"dynamics":[38],"networked":[41],"system":[42,65],"under":[43],"delayed":[44,161],"feedback":[45,162],"control.":[46],"Based":[47],"on":[48,97,107],"linear":[50],"stability":[51,58,75,109],"method":[52],"bifurcation":[55,71],"theorem,":[56],"equilibrium":[61,83],"error":[64],"existence":[68],"are":[72,116],"studied.":[73],"The":[74,113],"periodic":[77],"solutions":[78],"bifurcating":[79],"from":[80],"trivial":[82],"is":[84,96],"analyzed":[85],"using":[86],"normal":[87],"form":[88],"theory":[89],"central":[91],"manifold":[92],"theorem.":[93],"Special":[94],"focus":[95],"effects":[99],"topology":[103],"delays":[106],"bifurcation.":[112],"theoretical":[114,156],"results":[115,157],"also":[117],"extended":[118],"networks":[122],"with":[123],"asymmetric":[124],"adjacent":[125],"matrices.":[126],"addition,":[128],"controlled":[130],"model":[131],"exhibits":[132],"complicated":[133,170],"dynamical":[134],"behavior":[135,171],"via":[136],"three":[137],"types":[138],"codimension":[140],"two":[141],"bifurcations":[142,145],"period-doubling":[144],"that":[146,160],"eventually":[147],"lead":[148],"chaos.":[150],"Numerical":[151],"experiments":[152],"have":[153],"validated":[154],"indicated":[159],"control":[163],"can":[164],"effectively":[165],"or":[167],"annihilate":[168],"networks.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}