{"id":"https://openalex.org/W1966618180","doi":"https://doi.org/10.1142/s0218127412502859","title":"EXTENDING LOCAL PASSIVITY THEORY AND HOPF BIFURCATION AT THE EDGE OF CHAOS IN OREGONATOR CNN","display_name":"EXTENDING LOCAL PASSIVITY THEORY AND HOPF BIFURCATION AT THE EDGE OF CHAOS IN OREGONATOR CNN","publication_year":2012,"publication_date":"2012-11-01","ids":{"openalex":"https://openalex.org/W1966618180","doi":"https://doi.org/10.1142/s0218127412502859","mag":"1966618180"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127412502859","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502859","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/A5067116677","display_name":"Changbing Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"CHANGBING TANG","raw_affiliation_strings":["Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China"],"affiliations":[{"raw_affiliation_string":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088079072","display_name":"Fangyue Chen","orcid":"https://orcid.org/0000-0002-5440-3206"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FANGYUE CHEN","raw_affiliation_strings":["School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, Hangzhou 310018, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, Hangzhou 310018, P. R. China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039832052","display_name":"Jianbo Wang","orcid":"https://orcid.org/0000-0002-1479-3107"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIANBO WANG","raw_affiliation_strings":["Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China"],"affiliations":[{"raw_affiliation_string":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100674281","display_name":"Xiang Li","orcid":"https://orcid.org/0000-0002-6482-2535"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIANG LI","raw_affiliation_strings":["Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China"],"affiliations":[{"raw_affiliation_string":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5067116677"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0848553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"11","first_page":"1250285","last_page":"1250285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9995999932289124,"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":0.9995999932289124,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994999766349792,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/passivity","display_name":"Passivity","score":0.8843344449996948},{"id":"https://openalex.org/keywords/edge-of-chaos","display_name":"Edge of chaos","score":0.7461848855018616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.596068799495697},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5551552176475525},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.47654563188552856},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39898261427879333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35708945989608765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18783071637153625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09680339694023132},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08404463529586792}],"concepts":[{"id":"https://openalex.org/C2778809601","wikidata":"https://www.wikidata.org/wiki/Q1045736","display_name":"Passivity","level":2,"score":0.8843344449996948},{"id":"https://openalex.org/C2780713532","wikidata":"https://www.wikidata.org/wiki/Q93158","display_name":"Edge of chaos","level":2,"score":0.7461848855018616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.596068799495697},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5551552176475525},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.47654563188552856},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39898261427879333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35708945989608765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18783071637153625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09680339694023132},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08404463529586792},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127412502859","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502859","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W99253999","https://openalex.org/W625483316","https://openalex.org/W1509576544","https://openalex.org/W1531715726","https://openalex.org/W1570173134","https://openalex.org/W1964614740","https://openalex.org/W1971443020","https://openalex.org/W1987066381","https://openalex.org/W1988579997","https://openalex.org/W1993999944","https://openalex.org/W1995627131","https://openalex.org/W2018341541","https://openalex.org/W2028720893","https://openalex.org/W2045152679","https://openalex.org/W2052773149","https://openalex.org/W2056717940","https://openalex.org/W2063909743","https://openalex.org/W2076693861","https://openalex.org/W2094606883","https://openalex.org/W2095335384","https://openalex.org/W2095708000","https://openalex.org/W2107025852","https://openalex.org/W2112329999","https://openalex.org/W2112759202","https://openalex.org/W2126137056","https://openalex.org/W2136003379","https://openalex.org/W2153653041","https://openalex.org/W2160121923","https://openalex.org/W2162484124","https://openalex.org/W2167766297","https://openalex.org/W2170669616","https://openalex.org/W2171737037","https://openalex.org/W2171797266","https://openalex.org/W2292208776","https://openalex.org/W2357668496","https://openalex.org/W3013533083","https://openalex.org/W3089091070","https://openalex.org/W4292365908"],"related_works":["https://openalex.org/W2137413016","https://openalex.org/W2094046875","https://openalex.org/W110415256","https://openalex.org/W2069713792","https://openalex.org/W370258010","https://openalex.org/W4388906764","https://openalex.org/W2334634358","https://openalex.org/W2037413193","https://openalex.org/W2233462344","https://openalex.org/W2953100338"],"abstract_inverted_index":{"The":[0],"fundamental":[1],"local":[2,26,62,77,136],"passivity":[3,27,63,78,137],"theory":[4,79,138],"asserts":[5],"that":[6,114],"a":[7,31,39,96,123,149],"wide":[8],"spectrum":[9],"of":[10,85,95,103,106,131,148,156],"complex":[11],"behaviors":[12],"may":[13,121],"exist":[14],"if":[15,91,134,144],"the":[16,19,36,49,57,61,69,76,83,86,92,101,107,110,128,135,145,154,158],"cells":[17],"in":[18,38,118],"reaction\u2013diffusion":[20,124],"are":[21,98,151],"not":[22,140],"locally":[23],"passive.":[24],"This":[25],"principle":[28],"has":[29],"provided":[30],"powerful":[32],"tool":[33,58],"for":[34,59],"studying":[35],"complexity":[37,50],"homogeneous":[40],"lattice":[41],"formed":[42],"by":[43],"coupled":[44],"cells.":[45],"In":[46],"this":[47],"paper,":[48],"matrix":[51],"Y":[52],"Q":[53,73],"(s),":[54],"which":[55],"is":[56,65,80,139,160],"testing":[60],"theory,":[64],"modified":[66],"based":[67],"on":[68],"characteristic":[70],"polynomial":[71],"A":[72],"(\u03bb).":[74],"Then,":[75],"applied":[81],"to":[82,89],"study":[84],"Oregonator":[87,119],"CNN":[88,97,120,150],"judge":[90],"cell":[93,146],"parameters":[94,147],"chosen":[99,152],"at":[100,153],"edge":[102,155],"chaos.":[104],"Analysis":[105],"bifurcation":[108],"and":[109],"numerical":[111],"simulations":[112],"show":[113],"nonzero":[115],"diffusion":[116,132],"term":[117],"cause":[122],"equation":[125],"oscillating":[126],"under":[127],"appropriate":[129],"choice":[130],"coefficient":[133],"satisfied.":[141],"That":[142],"is,":[143],"chaos,":[157],"system":[159],"potentially":[161],"unstable.":[162]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
