{"id":"https://openalex.org/W4200342544","doi":"https://doi.org/10.1142/s0218127421502333","title":"Chaos in the Rulkov Neuron Model Based on Marotto\u2019s Theorem","display_name":"Chaos in the Rulkov Neuron Model Based on Marotto\u2019s Theorem","publication_year":2021,"publication_date":"2021-12-07","ids":{"openalex":"https://openalex.org/W4200342544","doi":"https://doi.org/10.1142/s0218127421502333"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421502333","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421502333","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/A5008313001","display_name":"Penghe Ge","orcid":"https://orcid.org/0009-0004-4897-5090"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Penghe Ge","raw_affiliation_strings":["Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101825666","display_name":"Hongjun Cao","orcid":"https://orcid.org/0000-0003-4625-5351"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongjun Cao","raw_affiliation_strings":["Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-4625-5351","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":null,"apc_paid":null,"fwci":0.1313,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.4886059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"15","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998000264167786,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9901999831199646,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.7011232972145081},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6042787432670593},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6022971272468567},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5569500923156738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.503555953502655},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.440092533826828},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3581213355064392},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34225994348526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3341726064682007},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3306991457939148},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.295376181602478},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.2353653609752655},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.17259225249290466},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15011811256408691},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12394165992736816}],"concepts":[{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.7011232972145081},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6042787432670593},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6022971272468567},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5569500923156738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.503555953502655},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.440092533826828},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3581213355064392},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34225994348526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3341726064682007},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3306991457939148},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.295376181602478},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.2353653609752655},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.17259225249290466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15011811256408691},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12394165992736816},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421502333","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421502333","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/G7215084153","display_name":null,"funder_award_id":"2020YJS175","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1983516483","https://openalex.org/W2001395894","https://openalex.org/W2015333868","https://openalex.org/W2021915072","https://openalex.org/W2024120216","https://openalex.org/W2024306217","https://openalex.org/W2032685556","https://openalex.org/W2041329344","https://openalex.org/W2043634669","https://openalex.org/W2049904810","https://openalex.org/W2065567304","https://openalex.org/W2089484854","https://openalex.org/W2095180732","https://openalex.org/W2104902344","https://openalex.org/W2167975780","https://openalex.org/W2531613500","https://openalex.org/W2770728867","https://openalex.org/W2907919179","https://openalex.org/W3114593111","https://openalex.org/W4256081943","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2982067450","https://openalex.org/W2026096788","https://openalex.org/W2025109898","https://openalex.org/W2376791928","https://openalex.org/W3183850587","https://openalex.org/W2082662197","https://openalex.org/W2028466298","https://openalex.org/W2092428612","https://openalex.org/W1536503843","https://openalex.org/W2611154064"],"abstract_inverted_index":{"The":[0],"existence":[1,39,120,135],"of":[2,19,29,40,121,124,136],"chaos":[3,83],"in":[4,66],"the":[5,16,20,27,30,38,45,62,68,75,100,119,134],"Rulkov":[6,46,102],"neuron":[7,47,103],"model":[8,21,48],"is":[9,49,106],"proved":[10,107],"based":[11],"on":[12,74],"Marotto\u2019s":[13],"theorem.":[14],"Firstly,":[15],"stability":[17],"conditions":[18,77],"are":[22,33],"briefly":[23],"renewed":[24],"through":[25],"analyzing":[26],"eigenvalues":[28],"model,":[31,104],"which":[32,67,127],"very":[34],"important":[35],"preconditions":[36],"for":[37,99],"a":[41,52,57,111,129,137],"snap-back":[42,80,112,138],"repeller.":[43,139],"Secondly,":[44],"decomposed":[50],"to":[51,132],"one-dimensional":[53,58],"fast":[54,69],"subsystem":[55,60,70],"and":[56,78,82,95],"slow":[59],"by":[61,87,117],"fast\u2013slow":[63],"dynamics":[64],"technique,":[65],"has":[71],"sensitive":[72],"dependence":[73],"initial":[76],"its":[79],"repeller":[81,113],"can":[84],"be":[85],"verified":[86],"numerical":[88],"methods,":[89],"such":[90],"as":[91],"waveforms,":[92],"Lyapunov":[93],"exponents,":[94],"bifurcation":[96],"diagrams.":[97],"Thirdly,":[98],"two-dimensional":[101],"it":[105],"that":[108],"there":[109],"exists":[110],"under":[114],"two":[115],"iterations":[116],"illustrating":[118],"an":[122],"intersection":[123],"three":[125],"surfaces,":[126],"pave":[128],"new":[130],"way":[131],"identify":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}