{"id":"https://openalex.org/W2023323873","doi":"https://doi.org/10.1142/s0218127405013575","title":"HOPF BIFURCATION AND CHAOS IN TABU LEARNING NEURON MODELS","display_name":"HOPF BIFURCATION AND CHAOS IN TABU LEARNING NEURON MODELS","publication_year":2005,"publication_date":"2005-08-01","ids":{"openalex":"https://openalex.org/W2023323873","doi":"https://doi.org/10.1142/s0218127405013575","mag":"2023323873"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013575","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013575","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/nlin/0411028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100654349","display_name":"Chunguang Li","orcid":"https://orcid.org/0000-0003-3147-1553"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"CHUNGUANG LI","raw_affiliation_strings":["Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"GUANRONG CHEN","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022342592","display_name":"Xiaofeng Liao","orcid":"https://orcid.org/0000-0002-3566-8161"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIAOFENG LIAO","raw_affiliation_strings":["Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100958777","display_name":"Juebang Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUEBANG YU","raw_affiliation_strings":["Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Electronic Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4068,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.86809763,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"15","issue":"08","first_page":"2633","last_page":"2642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9994000196456909,"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":0.9994000196456909,"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/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9970999956130981,"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/chaotic","display_name":"Chaotic","score":0.6610836386680603},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6302154064178467},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6082479953765869},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.5516812801361084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5430968403816223},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.473076194524765},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45105046033859253},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4445193409919739},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4306967854499817},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.4122304320335388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34305259585380554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29421401023864746},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.19435390830039978},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17087936401367188},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14159581065177917},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06130972504615784}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6610836386680603},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6302154064178467},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6082479953765869},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.5516812801361084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5430968403816223},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.473076194524765},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45105046033859253},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4445193409919739},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4306967854499817},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.4122304320335388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34305259585380554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29421401023864746},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.19435390830039978},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17087936401367188},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14159581065177917},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06130972504615784},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127405013575","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013575","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"},{"id":"pmh:oai:arXiv.org:nlin/0411028","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0411028","pdf_url":"https://arxiv.org/pdf/nlin/0411028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.3161","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.3161","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/nlin/0411028v1.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:nlin/0411028","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0411028","pdf_url":"https://arxiv.org/pdf/nlin/0411028","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1438394186","https://openalex.org/W1531715726","https://openalex.org/W1963913942","https://openalex.org/W1970381782","https://openalex.org/W1970680382","https://openalex.org/W1978212693","https://openalex.org/W2005914015","https://openalex.org/W2012501493","https://openalex.org/W2020604825","https://openalex.org/W2020975304","https://openalex.org/W2026468138","https://openalex.org/W2027673005","https://openalex.org/W2041341436","https://openalex.org/W2046986331","https://openalex.org/W2064340892","https://openalex.org/W2071952493","https://openalex.org/W2088685800","https://openalex.org/W2104670598","https://openalex.org/W2136680639","https://openalex.org/W2143719895","https://openalex.org/W2151497088","https://openalex.org/W2152254020","https://openalex.org/W4246598646"],"related_works":["https://openalex.org/W2246258018","https://openalex.org/W4296238711","https://openalex.org/W3105759999","https://openalex.org/W1833545828","https://openalex.org/W2137413016","https://openalex.org/W2393929457","https://openalex.org/W2094046875","https://openalex.org/W2713021514","https://openalex.org/W2319243846","https://openalex.org/W2762201087"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,34,76,93],"consider":[4,17],"the":[5,26,41,46,51,54,61,72,78,95],"nonlinear":[6],"dynamical":[7],"behaviors":[8,97],"of":[9,45,53],"some":[10],"tabu":[11,19,99],"learning":[12,20,100],"neuron":[13,22,84],"models.":[14],"We":[15,65],"first":[16],"a":[18,31,67,83],"single":[21],"model.":[23],"By":[24],"choosing":[25],"memory":[27],"decay":[28],"rate":[29],"as":[30],"bifurcation":[32,38,56],"parameter,":[33],"prove":[35],"that":[36],"Hopf":[37,55],"occurs":[39],"in":[40,81,98],"neuron.":[42],"The":[43],"stability":[44],"bifurcating":[47],"periodic":[48],"solutions":[49],"and":[50,105],"direction":[52],"are":[57],"determined":[58],"by":[59],"applying":[60],"normal":[62],"form":[63],"theory.":[64],"give":[66],"numerical":[68],"example":[69],"to":[70],"verify":[71],"theoretical":[73],"analysis.":[74],"Then,":[75],"demonstrate":[77],"chaotic":[79,96],"behavior":[80],"such":[82],"with":[85,103],"sinusoidal":[86],"external":[87],"input,":[88],"via":[89],"computer":[90],"simulations.":[91],"Finally,":[92],"study":[94],"two-neuron":[101],"models,":[102],"linear":[104],"quadratic":[106],"proximity":[107],"functions":[108],"respectively.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}