{"id":"https://openalex.org/W2782439591","doi":"https://doi.org/10.1142/s0218127417502091","title":"Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay","display_name":"Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay","publication_year":2017,"publication_date":"2017-12-15","ids":{"openalex":"https://openalex.org/W2782439591","doi":"https://doi.org/10.1142/s0218127417502091","mag":"2782439591"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417502091","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502091","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/A5100422268","display_name":"Zhen Wang","orcid":"https://orcid.org/0000-0001-7188-5828"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhen Wang","raw_affiliation_strings":["College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China","College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100455470","display_name":"Xiaohong Wang","orcid":"https://orcid.org/0000-0003-2371-2572"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohong Wang","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100736198","display_name":"Yuxia Li","orcid":"https://orcid.org/0000-0002-6069-2630"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuxia Li","raw_affiliation_strings":["College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080634329","display_name":"Xia Huang","orcid":"https://orcid.org/0000-0002-4955-8318"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xia Huang","raw_affiliation_strings":["College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, P. R. China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100422268","https://openalex.org/A5100736198"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":null,"apc_paid":null,"fwci":32.4046,"has_fulltext":false,"cited_by_count":200,"citation_normalized_percentile":{"value":0.99795933,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"27","issue":"13","first_page":"1750209","last_page":"1750209"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8373920321464539},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7691401839256287},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6312578320503235},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5765254497528076},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.5342046022415161},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5198788642883301},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4923819303512573},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4743158519268036},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.47270748019218445},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4451184868812561},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4389876425266266},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43627065420150757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4191821217536926},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3130677342414856},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15078383684158325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.093812495470047},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08100596070289612}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8373920321464539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7691401839256287},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6312578320503235},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5765254497528076},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.5342046022415161},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5198788642883301},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4923819303512573},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4743158519268036},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.47270748019218445},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4451184868812561},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4389876425266266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43627065420150757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4191821217536926},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3130677342414856},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15078383684158325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.093812495470047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08100596070289612},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417502091","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417502091","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":[{"id":"https://openalex.org/G2033286663","display_name":null,"funder_award_id":"61473177","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3588914096","display_name":null,"funder_award_id":"61573008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5800021139","display_name":null,"funder_award_id":"61473178","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W968732228","https://openalex.org/W1894922855","https://openalex.org/W1966636072","https://openalex.org/W1968134101","https://openalex.org/W1970680382","https://openalex.org/W1971609228","https://openalex.org/W1977225820","https://openalex.org/W1977447091","https://openalex.org/W1978524241","https://openalex.org/W1983581275","https://openalex.org/W1984796440","https://openalex.org/W2008244590","https://openalex.org/W2013188209","https://openalex.org/W2018282309","https://openalex.org/W2025808664","https://openalex.org/W2033470589","https://openalex.org/W2047515252","https://openalex.org/W2051054098","https://openalex.org/W2051137709","https://openalex.org/W2053751819","https://openalex.org/W2056904916","https://openalex.org/W2070706103","https://openalex.org/W2072338133","https://openalex.org/W2094551465","https://openalex.org/W2098524127","https://openalex.org/W2111025408","https://openalex.org/W2126728219","https://openalex.org/W2135082607","https://openalex.org/W2157077261","https://openalex.org/W2167797372","https://openalex.org/W2169006540","https://openalex.org/W2198475680","https://openalex.org/W2318896103","https://openalex.org/W2496175068","https://openalex.org/W2496913885","https://openalex.org/W2620499377","https://openalex.org/W2752740962","https://openalex.org/W2781501082","https://openalex.org/W2787959293","https://openalex.org/W3201154547","https://openalex.org/W4292692317","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2978098199","https://openalex.org/W2054978396","https://openalex.org/W2021742636","https://openalex.org/W4214875847","https://openalex.org/W2143208590","https://openalex.org/W2751270551","https://openalex.org/W4285005170","https://openalex.org/W3015096850","https://openalex.org/W4301195779"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,25,28,44,47,52,56,64,68,72,88,91],"problems":[4],"of":[5,13,27,31,46,67,74,90],"stability":[6,29,45],"and":[7,35,63],"Hopf":[8,59,75],"bifurcation":[9,57,60,76],"in":[10],"a":[11],"class":[12],"fractional-order":[14,32],"complex-valued":[15],"single":[16],"neuron":[17],"model":[18],"with":[19],"time":[20,53,69],"delay":[21,54,70],"are":[22,49,84],"addressed.":[23],"With":[24],"help":[26],"theory":[30],"differential":[33],"equations":[34],"Laplace":[36],"transforms,":[37],"several":[38],"new":[39],"sufficient":[40],"conditions,":[41],"which":[42],"ensure":[43],"system":[48],"derived.":[50],"Taking":[51],"as":[55],"parameter,":[58],"is":[61,77],"investigated":[62],"critical":[65],"value":[66],"for":[71],"occurrence":[73],"determined.":[78],"Finally,":[79],"two":[80],"representative":[81],"numerical":[82],"examples":[83],"given":[85],"to":[86],"show":[87],"effectiveness":[89],"theoretical":[92],"results.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":64},{"year":2018,"cited_by_count":52}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}