{"id":"https://openalex.org/W2108109772","doi":"https://doi.org/10.1007/s00332-009-9046-1","title":"Stability Switches, Hopf Bifurcations, and\u00a0Spatio-temporal Patterns in\u00a0a\u00a0Delayed Neural Model with\u00a0Bidirectional Coupling","display_name":"Stability Switches, Hopf Bifurcations, and\u00a0Spatio-temporal Patterns in\u00a0a\u00a0Delayed Neural Model with\u00a0Bidirectional Coupling","publication_year":2009,"publication_date":"2009-05-27","ids":{"openalex":"https://openalex.org/W2108109772","doi":"https://doi.org/10.1007/s00332-009-9046-1","mag":"2108109772"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-009-9046-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-009-9046-1","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","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/A5026187828","display_name":"Yongli Song","orcid":"https://orcid.org/0000-0002-2209-2458"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]},{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU","CN"],"is_corresponding":true,"raw_author_name":"Yongli Song","raw_affiliation_strings":["Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","Department of Mathematics, Tongji University, Shanghai, 200092, China","Curtin University of Technology","Tongji University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai, 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Curtin University of Technology","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Tongji University","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086628608","display_name":"Tonghua Zhang","orcid":"https://orcid.org/0000-0003-0510-1428"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Tonghua Zhang","raw_affiliation_strings":["Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","Curtin University of  Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Curtin University of  Technology","institution_ids":["https://openalex.org/I205640436"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069002414","display_name":"Moses O. Tad\u00e9","orcid":"https://orcid.org/0000-0001-6378-3274"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Moses O. Tad\u00e9","raw_affiliation_strings":["Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","Curtin University of  Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia","institution_ids":["https://openalex.org/I205640436"]},{"raw_affiliation_string":"Curtin University of  Technology","institution_ids":["https://openalex.org/I205640436"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026187828"],"corresponding_institution_ids":["https://openalex.org/I116953780","https://openalex.org/I205640436"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0892,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.79870607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"6","first_page":"597","last_page":"632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998000264167786,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998000264167786,"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/T11513","display_name":"stochastic dynamics and bifurcation","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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"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/center-manifold","display_name":"Center manifold","score":0.8180370330810547},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7042229175567627},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5995568037033081},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5800419449806213},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5787057876586914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.518657386302948},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5118429064750671},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.42933475971221924},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3635464906692505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3553857207298279},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3364279270172119},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3268882632255554},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1836824119091034},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09860286116600037},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08739396929740906}],"concepts":[{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.8180370330810547},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7042229175567627},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5995568037033081},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5800419449806213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5787057876586914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.518657386302948},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5118429064750671},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.42933475971221924},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3635464906692505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3553857207298279},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3364279270172119},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3268882632255554},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1836824119091034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09860286116600037},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08739396929740906},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00332-009-9046-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-009-9046-1","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/43436","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11937/43436","pdf_url":null,"source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"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":"Journal Article"},{"id":"pmh:oai:researchbank.swinburne.edu.au:8488c283-8fd9-47bf-9193-be084d7aab7a/1","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.3/192078","pdf_url":null,"source":{"id":"https://openalex.org/S4306401157","display_name":"Swinburne Research Bank (Swinburne University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I57093077","host_organization_name":"Swinburne University of Technology","host_organization_lineage":["https://openalex.org/I57093077"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Nonlinear Science, Vol. 19, no. 6 (Dec 2009), pp. 597-632","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321881","display_name":"Shanghai Municipal Education Commission","ror":"https://ror.org/05tewj457"},{"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":46,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W161994494","https://openalex.org/W1504546061","https://openalex.org/W1552317631","https://openalex.org/W1577873058","https://openalex.org/W1603340857","https://openalex.org/W1607633954","https://openalex.org/W1965778005","https://openalex.org/W1970189994","https://openalex.org/W1970964221","https://openalex.org/W1974416149","https://openalex.org/W1990303997","https://openalex.org/W1991380410","https://openalex.org/W1994162361","https://openalex.org/W2003302378","https://openalex.org/W2009433941","https://openalex.org/W2017634972","https://openalex.org/W2018815721","https://openalex.org/W2019027784","https://openalex.org/W2020174839","https://openalex.org/W2020975304","https://openalex.org/W2026174587","https://openalex.org/W2033270072","https://openalex.org/W2035033442","https://openalex.org/W2035310523","https://openalex.org/W2037037095","https://openalex.org/W2046076589","https://openalex.org/W2048419276","https://openalex.org/W2049929575","https://openalex.org/W2050514524","https://openalex.org/W2060813275","https://openalex.org/W2062210472","https://openalex.org/W2064340892","https://openalex.org/W2064534817","https://openalex.org/W2075555669","https://openalex.org/W2078089188","https://openalex.org/W2084772782","https://openalex.org/W2088685800","https://openalex.org/W2091679668","https://openalex.org/W2157036539","https://openalex.org/W2163284349","https://openalex.org/W2167797372","https://openalex.org/W2170709570","https://openalex.org/W2468443503","https://openalex.org/W3148499377","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W2038701038","https://openalex.org/W1975783007","https://openalex.org/W1996991127","https://openalex.org/W2382752082","https://openalex.org/W1988489950","https://openalex.org/W1986426368","https://openalex.org/W2363522146","https://openalex.org/W2061491569"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}