{"id":"https://openalex.org/W4323046206","doi":"https://doi.org/10.3390/axioms12030261","title":"Slow Manifolds for Stochastic Koper Models with Stable L\u00e9vy Noises","display_name":"Slow Manifolds for Stochastic Koper Models with Stable L\u00e9vy Noises","publication_year":2023,"publication_date":"2023-03-03","ids":{"openalex":"https://openalex.org/W4323046206","doi":"https://doi.org/10.3390/axioms12030261"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12030261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030261","pdf_url":"https://www.mdpi.com/2075-1680/12/3/261/pdf?version=1677824367","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/3/261/pdf?version=1677824367","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049225376","display_name":"Hina Zulfiqar","orcid":"https://orcid.org/0000-0002-1903-381X"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Hina Zulfiqar","raw_affiliation_strings":["Department of Mathematics, University of Okara, Okara 56300, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1903-381X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Okara, Okara 56300, Pakistan","institution_ids":["https://openalex.org/I3130814776"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088058310","display_name":"Shenglan Yuan","orcid":"https://orcid.org/0000-0002-4427-7795"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN","DE"],"is_corresponding":true,"raw_author_name":"Shenglan Yuan","raw_affiliation_strings":["Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China","Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4427-7795","affiliations":[{"raw_affiliation_string":"Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060234934","display_name":"Muhammad Shoaib Saleem","orcid":"https://orcid.org/0000-0002-0050-6760"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shoaib Saleem","raw_affiliation_strings":["Department of Mathematics, University of Okara, Okara 56300, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Okara, Okara 56300, Pakistan","institution_ids":["https://openalex.org/I3130814776"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088058310"],"corresponding_institution_ids":["https://openalex.org/I179225836","https://openalex.org/I47720641"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.1285,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36740521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"3","first_page":"261","last_page":"261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9994000196456909,"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":0.9994000196456909,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9944999814033508,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.7104133367538452},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6629678010940552},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5068512558937073},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5047625303268433},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49968457221984863},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.48575571179389954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4851313531398773},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4763627052307129},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4701184034347534},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4463408291339874},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4320247769355774},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4188503623008728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37698841094970703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27693092823028564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24518367648124695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20574796199798584},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.19178372621536255},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12834089994430542},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09213805198669434}],"concepts":[{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.7104133367538452},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6629678010940552},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5068512558937073},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5047625303268433},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49968457221984863},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.48575571179389954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4851313531398773},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4763627052307129},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4701184034347534},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4463408291339874},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4320247769355774},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4188503623008728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37698841094970703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27693092823028564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24518367648124695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20574796199798584},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.19178372621536255},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12834089994430542},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09213805198669434},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms12030261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030261","pdf_url":"https://www.mdpi.com/2075-1680/12/3/261/pdf?version=1677824367","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:103461","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103461","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/103461/103461.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:0efc2934441b43d78d8d98f050f556b2","is_oa":true,"landing_page_url":"https://doaj.org/article/0efc2934441b43d78d8d98f050f556b2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 3, p 261 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/3/261/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12030261","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 3; Pages: 261","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12030261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030261","pdf_url":"https://www.mdpi.com/2075-1680/12/3/261/pdf?version=1677824367","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4323046206.pdf","grobid_xml":"https://content.openalex.org/works/W4323046206.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1531441528","https://openalex.org/W1983416177","https://openalex.org/W1995522593","https://openalex.org/W2003442039","https://openalex.org/W2027447627","https://openalex.org/W2040463943","https://openalex.org/W2043332585","https://openalex.org/W2047962726","https://openalex.org/W2058962910","https://openalex.org/W2064692957","https://openalex.org/W2075438738","https://openalex.org/W2523158257","https://openalex.org/W2526281083","https://openalex.org/W2913544682","https://openalex.org/W2917634716","https://openalex.org/W2921925230","https://openalex.org/W2963070862","https://openalex.org/W2963483013","https://openalex.org/W2971812236","https://openalex.org/W2991376678","https://openalex.org/W3022439851","https://openalex.org/W3103931584","https://openalex.org/W3105688030","https://openalex.org/W3135686425","https://openalex.org/W3166727831","https://openalex.org/W3166920304","https://openalex.org/W3176602066","https://openalex.org/W3205322541","https://openalex.org/W4206151608","https://openalex.org/W4241682055","https://openalex.org/W4290744579","https://openalex.org/W4296665311","https://openalex.org/W4312221399","https://openalex.org/W6727596410","https://openalex.org/W6751727002","https://openalex.org/W6757884579"],"related_works":["https://openalex.org/W2592405099","https://openalex.org/W2012002054","https://openalex.org/W2783536463","https://openalex.org/W2888156545","https://openalex.org/W2041424614","https://openalex.org/W3036909545","https://openalex.org/W3198656036","https://openalex.org/W2011117899","https://openalex.org/W3192449753","https://openalex.org/W1996603898"],"abstract_inverted_index":{"The":[0],"Koper":[1,33,48],"model":[2,34,49],"is":[3],"a":[4,31,46],"vector":[5],"field":[6],"in":[7,17],"which":[8],"the":[9,13,24,27,42,67],"differential":[10],"equations":[11],"describe":[12],"electrochemical":[14],"oscillations":[15],"appearing":[16],"diffusion":[18],"processes.":[19],"This":[20],"work":[21],"focuses":[22],"on":[23],"understanding":[25],"of":[26,30],"slow":[28,43],"dynamics":[29],"stochastic":[32,47],"perturbed":[35],"by":[36],"stable":[37,51],"L\u00e9vy":[38,52],"noise.":[39],"We":[40,59],"establish":[41],"manifold":[44],"for":[45],"with":[50,70],"noise":[53],"and":[54],"verify":[55],"exponential":[56],"tracking":[57],"properties.":[58],"also":[60],"present":[61],"two":[62],"practical":[63],"examples":[64],"to":[65],"demonstrate":[66],"analytical":[68],"results":[69],"numerical":[71],"simulations.":[72]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2023-03-04T00:00:00"}
