{"id":"https://openalex.org/W1994162361","doi":"https://doi.org/10.1137/s0036141001386519","title":"Nonlinear Waves in Networks of Neurons with Delayed Feedback: Pattern Formation and Continuation","display_name":"Nonlinear Waves in Networks of Neurons with Delayed Feedback: Pattern Formation and Continuation","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1994162361","doi":"https://doi.org/10.1137/s0036141001386519","mag":"1994162361"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141001386519","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001386519","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/A5103418445","display_name":"Lihong Huang","orcid":"https://orcid.org/0000-0002-7294-9587"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lihong Huang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Jianhong Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jianhong Wu","raw_affiliation_strings":["York University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"York University","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4848,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.91067961,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"34","issue":"4","first_page":"836","last_page":"860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9987999796867371,"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":0.9952999949455261,"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":0.8666455745697021},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6874730587005615},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6720223426818848},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6234238743782043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5811475515365601},{"id":"https://openalex.org/keywords/invariance-principle","display_name":"Invariance principle","score":0.4762720763683319},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4562995135784149},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.41394418478012085},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32010915875434875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8666455745697021},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6874730587005615},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6720223426818848},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6234238743782043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5811475515365601},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.4762720763683319},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4562995135784149},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.41394418478012085},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32010915875434875},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141001386519","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001386519","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":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W313143230","https://openalex.org/W359361325","https://openalex.org/W576136270","https://openalex.org/W1510122527","https://openalex.org/W1551791849","https://openalex.org/W1552317631","https://openalex.org/W1565432736","https://openalex.org/W1603235397","https://openalex.org/W1607633954","https://openalex.org/W1937028141","https://openalex.org/W1964053068","https://openalex.org/W1965778005","https://openalex.org/W1988026848","https://openalex.org/W2000850384","https://openalex.org/W2003578553","https://openalex.org/W2020174839","https://openalex.org/W2046658120","https://openalex.org/W2056812907","https://openalex.org/W2062210787","https://openalex.org/W2064971633","https://openalex.org/W2065450947","https://openalex.org/W2067294365","https://openalex.org/W2079871064","https://openalex.org/W2087064550","https://openalex.org/W2088959696","https://openalex.org/W2091679668","https://openalex.org/W2112246162","https://openalex.org/W2147502381","https://openalex.org/W2397880101","https://openalex.org/W4210417410","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W1552317631","https://openalex.org/W2020174839","https://openalex.org/W1970964221","https://openalex.org/W1970189994","https://openalex.org/W2000260888","https://openalex.org/W2112246162","https://openalex.org/W1965778005","https://openalex.org/W1607633954","https://openalex.org/W2075555669","https://openalex.org/W2064534817","https://openalex.org/W2060813275","https://openalex.org/W2049929575","https://openalex.org/W2048676671","https://openalex.org/W2022601797","https://openalex.org/W2020975304","https://openalex.org/W2009433941","https://openalex.org/W2064340892","https://openalex.org/W2037037095","https://openalex.org/W2065134213","https://openalex.org/W2046076589"],"abstract_inverted_index":{"An":[0],"on-center":[1],"off-surround":[2],"network":[3],"of":[4,16,19,29,37,40,60,68],"three":[5],"identical":[6],"neurons":[7],"with":[8,65],"delayed":[9],"feedback":[10],"is":[11,32,43],"considered,":[12],"and":[13,26,45,49,81],"the":[14,23,56],"effect":[15],"synaptic":[17],"delay":[18,61],"signal":[20],"transmission":[21],"on":[22],"pattern":[24],"formation":[25],"global":[27],"continuation":[28],"nonlinear":[30],"waves":[31],"described.":[33],"The":[34],"spontaneous":[35],"bifurcation":[36,58],"multiple":[38],"branches":[39],"periodic":[41],"solutions":[42],"discussed,":[44],"their":[46],"spatio-temporal":[47],"patterns":[48],"mode":[50],"interactions":[51],"are":[52],"studied":[53],"by":[54],"using":[55],"symmetric":[57],"theory":[59,67],"differential":[62,82],"equations":[63],"coupled":[64],"representation":[66],"standard":[69],"dihedral":[70],"groups,":[71],"Liapunov's":[72],"direct":[73],"method,":[74],"LaSalle's":[75],"invariance":[76],"principle,":[77],"a":[78],"priori":[79],"estimates,":[80],"inequalities.":[83]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}