{"id":"https://openalex.org/W4415722017","doi":"https://doi.org/10.3390/axioms14110808","title":"Stability and Controllability of Nonlinear Dynamic Systems with Neural Networks: An Application to Financial Data","display_name":"Stability and Controllability of Nonlinear Dynamic Systems with Neural Networks: An Application to Financial Data","publication_year":2025,"publication_date":"2025-10-30","ids":{"openalex":"https://openalex.org/W4415722017","doi":"https://doi.org/10.3390/axioms14110808"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14110808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110808","pdf_url":"https://www.mdpi.com/2075-1680/14/11/808/pdf?version=1761832846","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/2075-1680/14/11/808/pdf?version=1761832846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120197885","display_name":"Lamiae Seddati","orcid":null},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Lamiae Seddati","raw_affiliation_strings":["Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033856969","display_name":"Touria Karite","orcid":"https://orcid.org/0000-0002-7074-764X"},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Touria Karite","raw_affiliation_strings":["Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco"],"raw_orcid":"https://orcid.org/0000-0002-7074-764X","affiliations":[{"raw_affiliation_string":"Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101620518","display_name":"Ahmed Aberqi","orcid":"https://orcid.org/0000-0003-3599-9099"},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Ahmed Aberqi","raw_affiliation_strings":["Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco"],"raw_orcid":"https://orcid.org/0000-0003-3599-9099","affiliations":[{"raw_affiliation_string":"Laboratory of Applied Sciences & Emerging Technologies (LSATE), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d\u2019Imouzzer, Fez BP 72, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036397819","display_name":"Nuno R. O. Bastos","orcid":"https://orcid.org/0000-0003-1533-1075"},"institutions":[{"id":"https://openalex.org/I56125125","display_name":"Polytechnic Institute of Viseu","ror":"https://ror.org/0235kxk33","country_code":"PT","type":"education","lineage":["https://openalex.org/I56125125"]},{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Nuno R. O. Bastos","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal","School of Technology and Management of Viseu, Polytechnic Institute of Viseu, Campus Polit\u00e9cnico, 3504-510 Viseu, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]},{"raw_affiliation_string":"School of Technology and Management of Viseu, Polytechnic Institute of Viseu, Campus Polit\u00e9cnico, 3504-510 Viseu, Portugal","institution_ids":["https://openalex.org/I56125125"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5036397819"],"corresponding_institution_ids":["https://openalex.org/I56125125","https://openalex.org/I60858718"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21689876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"11","first_page":"808","last_page":"808"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.2054000049829483,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.2054000049829483,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.18619999289512634,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.10610000044107437,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8273000121116638},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7189000248908997},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6306999921798706},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5641999840736389},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.5619000196456909},{"id":"https://openalex.org/keywords/adaptability","display_name":"Adaptability","score":0.5357000231742859},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4738999903202057},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.446399986743927}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8273000121116638},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7189000248908997},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6306999921798706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5907999873161316},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5641999840736389},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.5619000196456909},{"id":"https://openalex.org/C177606310","wikidata":"https://www.wikidata.org/wiki/Q5674297","display_name":"Adaptability","level":2,"score":0.5357000231742859},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3894999921321869},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.36239999532699585},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.31929999589920044},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2930999994277954},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.2651999890804291}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14110808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110808","pdf_url":"https://www.mdpi.com/2075-1680/14/11/808/pdf?version=1761832846","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:doaj.org/article:ac2b5b10c4d945c99fb6aa329f3e8ad2","is_oa":true,"landing_page_url":"https://doaj.org/article/ac2b5b10c4d945c99fb6aa329f3e8ad2","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 14, Iss 11, p 808 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14110808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110808","pdf_url":"https://www.mdpi.com/2075-1680/14/11/808/pdf?version=1761832846","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":[{"id":"https://openalex.org/G253191505","display_name":null,"funder_award_id":"UID/4106/2025","funder_id":"https://openalex.org/F4320329951","funder_display_name":"Center for Research and Development in Mathematics and Applications"},{"id":"https://openalex.org/G3659559413","display_name":null,"funder_award_id":"UID/4106/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3929736893","display_name":null,"funder_award_id":"UID/PRR/4106/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G7851690062","display_name":null,"funder_award_id":"UID/PRR/4106/2025","funder_id":"https://openalex.org/F4320329951","funder_display_name":"Center for Research and Development in Mathematics and Applications"}],"funders":[{"id":"https://openalex.org/F4320329951","display_name":"Center for Research and Development in Mathematics and Applications","ror":null},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415722017.pdf","grobid_xml":"https://content.openalex.org/works/W4415722017.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1498436455","https://openalex.org/W1597286183","https://openalex.org/W1988837728","https://openalex.org/W1989767494","https://openalex.org/W2015113370","https://openalex.org/W2054708090","https://openalex.org/W2055606008","https://openalex.org/W2056717940","https://openalex.org/W2062063134","https://openalex.org/W2065134213","https://openalex.org/W2066617143","https://openalex.org/W2087831875","https://openalex.org/W2112246162","https://openalex.org/W2116968117","https://openalex.org/W2128084896","https://openalex.org/W2160121923","https://openalex.org/W4253667136","https://openalex.org/W4400767527","https://openalex.org/W4404024513","https://openalex.org/W4404369417","https://openalex.org/W4409094742","https://openalex.org/W4409342342","https://openalex.org/W4410176758","https://openalex.org/W4411507771"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,20,96,101],"novel":[4],"approach":[5],"to":[6,109],"the":[7,34,68,79,110,115,121],"controllability":[8,26],"of":[9,36,106,114,123],"nonlinear":[10,130],"dynamic":[11],"systems":[12],"using":[13,64],"recurrent":[14],"neural":[15,124],"networks":[16],"(RNNs).":[17],"We":[18,88],"develop":[19],"comprehensive":[21],"theoretical":[22,50],"framework":[23,76],"that":[24],"integrates":[25],"analysis,":[27],"stability":[28],"verification":[29],"via":[30],"Lyapunov":[31],"functions,":[32],"and":[33,85,100,112],"derivation":[35],"optimal":[37],"control":[38,75,98,116,126],"laws":[39],"based":[40],"on":[41],"Pontryagin\u2019s":[42],"Maximum":[43],"Principle.":[44],"Our":[45],"methodology":[46],"not":[47],"only":[48],"ensures":[49],"soundness":[51],"but":[52],"also":[53],"offers":[54],"practical":[55],"effectiveness.":[56],"To":[57],"demonstrate":[58],"its":[59],"applicability,":[60],"we":[61],"conduct":[62],"simulations":[63],"real-world":[65],"data":[66],"from":[67],"AAPL":[69],"stock":[70],"database.":[71],"The":[72],"proposed":[73],"RNN-based":[74],"significantly":[77],"reduces":[78],"deviation":[80],"between":[81],"predicted":[82],"system":[83],"outputs":[84],"actual":[86],"observations.":[87],"further":[89],"enhance":[90],"performance":[91],"through":[92],"two":[93],"complementary":[94],"strategies,":[95],"direct":[97],"method":[99],"parameter":[102],"optimization":[103],"approach,":[104],"both":[105],"which":[107],"contribute":[108],"accuracy":[111],"adaptability":[113],"system.":[117],"These":[118],"results":[119],"confirm":[120],"potential":[122],"network-based":[125],"in":[127],"managing":[128],"complex":[129],"dynamics":[131]},"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-31T00:00:00"}