{"id":"https://openalex.org/W2041073870","doi":"https://doi.org/10.1142/s0218127407017987","title":"DYNAMICAL BEHAVIOR OF THE ALMOST-PERIODIC DISCRETE FITZHUGH\u2013NAGUMO SYSTEMS","display_name":"DYNAMICAL BEHAVIOR OF THE ALMOST-PERIODIC DISCRETE FITZHUGH\u2013NAGUMO SYSTEMS","publication_year":2007,"publication_date":"2007-05-01","ids":{"openalex":"https://openalex.org/W2041073870","doi":"https://doi.org/10.1142/s0218127407017987","mag":"2041073870"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407017987","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407017987","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/A5100369576","display_name":"Bixiang Wang","orcid":"https://orcid.org/0000-0001-5851-2453"},"institutions":[{"id":"https://openalex.org/I207123951","display_name":"New Mexico Institute of Mining and Technology","ror":"https://ror.org/005p9kw61","country_code":"US","type":"education","lineage":["https://openalex.org/I207123951"]},{"id":"https://openalex.org/I4210160338","display_name":"Mining Institute","ror":"https://ror.org/04x7sgz22","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210148470","https://openalex.org/I4210160338","https://openalex.org/I4210163714"]}],"countries":["RU","US"],"is_corresponding":true,"raw_author_name":"BIXIANG WANG","raw_affiliation_strings":["Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA","Supported in part by the Start-up Fund of New Mexico Institute of Mining and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA","institution_ids":["https://openalex.org/I207123951"]},{"raw_affiliation_string":"Supported in part by the Start-up Fund of New Mexico Institute of Mining and Technology","institution_ids":["https://openalex.org/I4210160338"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100369576"],"corresponding_institution_ids":["https://openalex.org/I207123951","https://openalex.org/I4210160338"],"apc_list":null,"apc_paid":null,"fwci":0.3324,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.65364453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"05","first_page":"1673","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.98580002784729,"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/attractor","display_name":"Attractor","score":0.8375643491744995},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7282480597496033},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.7262511849403381},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6737295985221863},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6146246194839478},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6095790863037109},{"id":"https://openalex.org/keywords/uniform-continuity","display_name":"Uniform continuity","score":0.5849997401237488},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5076407194137573},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.43586355447769165},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13940975069999695}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8375643491744995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7282480597496033},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.7262511849403381},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6737295985221863},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6146246194839478},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6095790863037109},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.5849997401237488},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5076407194137573},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.43586355447769165},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13940975069999695},{"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/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127407017987","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407017987","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1964953733","https://openalex.org/W1968267631","https://openalex.org/W1969040498","https://openalex.org/W1970739133","https://openalex.org/W1971564483","https://openalex.org/W1976792869","https://openalex.org/W1979386794","https://openalex.org/W1982406325","https://openalex.org/W1989420382","https://openalex.org/W1993693726","https://openalex.org/W2003128769","https://openalex.org/W2009375605","https://openalex.org/W2015298174","https://openalex.org/W2019038107","https://openalex.org/W2037171194","https://openalex.org/W2037273780","https://openalex.org/W2040389821","https://openalex.org/W2046851382","https://openalex.org/W2061191702","https://openalex.org/W2065148499","https://openalex.org/W2066926166","https://openalex.org/W2068597145","https://openalex.org/W2078823919","https://openalex.org/W2081923999","https://openalex.org/W2100457950","https://openalex.org/W2103893462","https://openalex.org/W2120081882","https://openalex.org/W2494583914","https://openalex.org/W2560896015","https://openalex.org/W2956114328","https://openalex.org/W3123164624","https://openalex.org/W4246012909"],"related_works":["https://openalex.org/W1637727067","https://openalex.org/W2037223594","https://openalex.org/W4255071521","https://openalex.org/W4388027594","https://openalex.org/W2032027650","https://openalex.org/W2460935991","https://openalex.org/W2013641432","https://openalex.org/W4240463762","https://openalex.org/W2358691237","https://openalex.org/W2281936874"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,21,37,45,52,78,94,109,114,117],"dynamical":[6],"behavior":[7],"of":[8,39,48,60,80,96,113,120],"nonautonomous,":[9],"almost-periodic":[10],"discrete":[11],"FitzHugh\u2013Nagumo":[12],"system":[13,24,54,115],"defined":[14],"on":[15,67],"infinite":[16],"lattices.":[17],"We":[18,42],"prove":[19],"that":[20],"nonautonomous":[22],"infinite-dimensional":[23,53],"has":[25],"a":[26,58,68,104],"uniform":[27,49,69,100,110],"attractor":[28],"which":[29,72],"attracts":[30],"all":[31],"solutions":[32,81],"uniformly":[33,83],"with":[34,85],"respect":[35,86],"to":[36,87],"translations":[38,95],"external":[40,97],"terms.":[41,98],"also":[43],"establish":[44],"upper":[46,118],"semicontinuity":[47,119],"attractors":[50],"when":[51],"is":[55,65],"approached":[56],"by":[57],"family":[59],"finite-dimensional":[61],"systems.":[62],"This":[63],"paper":[64],"based":[66],"tail":[70,101],"method,":[71],"shows":[73],"that,":[74],"for":[75,107],"large":[76],"time,":[77],"tails":[79],"are":[82],"small":[84],"bounded":[88],"initial":[89],"data":[90],"as":[91,93],"well":[92],"The":[99],"estimates":[102],"play":[103],"crucial":[105],"role":[106],"proving":[108],"asymptotic":[111],"compactness":[112],"and":[116],"attractors.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}