{"id":"https://openalex.org/W2965176705","doi":"https://doi.org/10.1142/s0218127419501116","title":"Complex Canard Explosion in a Fractional-Order FitzHugh\u2013Nagumo Model","display_name":"Complex Canard Explosion in a Fractional-Order FitzHugh\u2013Nagumo Model","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2965176705","doi":"https://doi.org/10.1142/s0218127419501116","mag":"2965176705"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419501116","doi":"https://doi.org/10.1142/s0218127419501116","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501116","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03041670","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059749882","display_name":"Mohammed-Salah Abdelouahab","orcid":"https://orcid.org/0000-0002-9235-8362","observed_orcids":["https://orcid.org/0000-0002-9235-8362"]},"institutions":[{"id":"https://openalex.org/I4210155582","display_name":"Centre Universitaire de Mila","ror":"https://ror.org/05s3cw058","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210155582"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mohammed-Salah Abdelouahab","raw_affiliation_strings":["Laboratory of Mathematics and Their Interactions, University Center of Mila, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Their Interactions, University Center of Mila, Algeria","institution_ids":["https://openalex.org/I4210155582"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076087931","display_name":"Ren\u00e9 Lozi","orcid":"https://orcid.org/0000-0003-0451-4255","observed_orcids":["https://orcid.org/0000-0003-0451-4255"]},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Lozi","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques J.A. Dieudonn\u00e9, Universit\u00e9 C\u00f4te d\u2019Azur, Parc Valrose, 06108 Nice Cedex 02, France"],"raw_orcid":"https://orcid.org/0000-0003-0451-4255","affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques J.A. Dieudonn\u00e9, Universit\u00e9 C\u00f4te d\u2019Azur, Parc Valrose, 06108 Nice Cedex 02, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I4210112930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418","observed_orcids":["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 Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1371,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.95300723,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"29","issue":"08","first_page":"1950111","last_page":"1950111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.6151999831199646,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.6151999831199646,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.1542000025510788,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.05770000070333481,"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/canard-explosion","display_name":"canard explosion","score":0.9860000014305115},{"id":"https://openalex.org/keywords/mixed-mode-oscillations","display_name":"mixed-mode oscillations","score":0.9290000200271606},{"id":"https://openalex.org/keywords/fractional-order-systems","display_name":"fractional-order systems","score":0.8019999861717224},{"id":"https://openalex.org/keywords/small-oscillations","display_name":"small oscillations","score":0.7129999995231628},{"id":"https://openalex.org/keywords/neural-dynamics","display_name":"neural dynamics","score":0.6930000185966492},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.33799999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5576671957969666},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5359590649604797},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.534397304058075},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5303345918655396},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4998817443847656},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.46931836009025574},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.431466281414032},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4259563684463501},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.42554253339767456},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4210323989391327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39519983530044556},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38274937868118286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3451188802719116},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32921522855758667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15856191515922546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09678387641906738},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127419501116","doi":"https://doi.org/10.1142/s0218127419501116","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501116","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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:HAL:hal-03041670v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-03041670","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.worldscientific.com/page/ijbc/editorial-board","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03041670v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-03041670","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.worldscientific.com/page/ijbc/editorial-board","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W93484778","https://openalex.org/W232893681","https://openalex.org/W1131478117","https://openalex.org/W1584611818","https://openalex.org/W1968859574","https://openalex.org/W1973909460","https://openalex.org/W1985940938","https://openalex.org/W1995299211","https://openalex.org/W2006109372","https://openalex.org/W2008052025","https://openalex.org/W2008187346","https://openalex.org/W2009375605","https://openalex.org/W2010835136","https://openalex.org/W2012613827","https://openalex.org/W2012748134","https://openalex.org/W2025068047","https://openalex.org/W2034058244","https://openalex.org/W2034651058","https://openalex.org/W2035651162","https://openalex.org/W2061191702","https://openalex.org/W2061686082","https://openalex.org/W2072774369","https://openalex.org/W2082275537","https://openalex.org/W2088614761","https://openalex.org/W2103678332","https://openalex.org/W2130079549","https://openalex.org/W2134837756","https://openalex.org/W2156367245","https://openalex.org/W2169938087","https://openalex.org/W2171030850","https://openalex.org/W2294239831","https://openalex.org/W2759077604","https://openalex.org/W2787959293","https://openalex.org/W2790249467","https://openalex.org/W2795694083","https://openalex.org/W4212878953","https://openalex.org/W4214513274","https://openalex.org/W4245296879","https://openalex.org/W4247953052","https://openalex.org/W4292994524"],"related_works":["https://openalex.org/W3102147451","https://openalex.org/W2994465894","https://openalex.org/W2621366651","https://openalex.org/W7153706069","https://openalex.org/W4286383039","https://openalex.org/W2759077604","https://openalex.org/W7056632749","https://openalex.org/W160309187","https://openalex.org/W3099801311","https://openalex.org/W3213123748"],"abstract_inverted_index":{"This":[0],"article":[1,176],"investigates":[2],"the":[3,22,25,46,62,69,72,76,79,87,103,109,130,141,167,175,179,194],"complex":[4,195],"phenomena":[5],"of":[6,24,61,71,78,83,89,111,114,122,129,137,197],"canard":[7,84,105],"explosion":[8,106],"with":[9,118,166,188],"mixed-mode":[10],"oscillations,":[11],"observed":[12],"from":[13],"a":[14,28,42,49,97,160,183],"fractional-order":[15,63,162],"FitzHugh\u2013Nagumo":[16],"(FFHN)":[17],"model.":[18],"To":[19],"rigorously":[20],"analyze":[21],"dynamics":[23,196],"FFHN":[26,73,131,180],"model,":[27],"new":[29,98],"mathematical":[30],"notion,":[31],"referred":[32,100],"to":[33,101,171,192],"as":[34,66,68,102],"Hopf-like":[35],"bifurcation":[36],"(HLB),":[37],"is":[38,116,153,182],"introduced.":[39],"HLB":[40,91],"provides":[41],"precise":[43],"definition":[44],"for":[45],"change":[47],"between":[48],"fixed":[50],"point":[51],"and":[52,75],"an":[53,119,189],"[Formula:":[54,57],"see":[55,58],"text]-asymptotically":[56],"text]-periodic":[59],"solution":[60],"dynamical":[64,164],"system,":[65,165],"well":[67],"stability":[70],"model":[74,132,181,187],"appearance":[77,110],"HLB.":[80],"The":[81,135],"existence":[82],"oscillations":[85,124,139],"in":[86,159],"neighborhoods":[88],"such":[90,138],"points":[92],"are":[93,133,145],"numerically":[94],"investigated.":[95],"Using":[96],"algorithm,":[99,108],"global-local":[104],"search":[107],"various":[112],"patterns":[113],"solutions":[115],"revealed,":[117],"increasing":[120],"number":[121],"small-amplitude":[123],"when":[125],"two":[126,142],"key":[127],"parameters":[128],"varied.":[134],"numbers":[136],"versus":[140],"parameters,":[143],"respectively,":[144],"perfectly":[146],"fitted":[147],"using":[148],"exponential":[149],"functions.":[150],"Finally,":[151],"it":[152],"conjectured":[154],"that":[155,178],"chaos":[156],"could":[157],"occur":[158],"two-dimensional":[161,186],"autonomous":[163],"fractional":[168],"order":[169],"close":[170],"one.":[172],"After":[173],"all,":[174],"demonstrates":[177],"very":[184],"simple":[185],"incredible":[190],"ability":[191],"present":[193],"neurons.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2019-08-13T00:00:00"}