{"id":"https://openalex.org/W4389764994","doi":"https://doi.org/10.33619/2414-2948/97/01","title":"The Phenomenon of Delaying Loss of Stability in the Theory of Singular Perturbations","display_name":"The Phenomenon of Delaying Loss of Stability in the Theory of Singular Perturbations","publication_year":2023,"publication_date":"2023-12-14","ids":{"openalex":"https://openalex.org/W4389764994","doi":"https://doi.org/10.33619/2414-2948/97/01"},"language":"en","primary_location":{"id":"doi:10.33619/2414-2948/97/01","doi":"https://doi.org/10.33619/2414-2948/97/01","is_oa":true,"landing_page_url":"https://doi.org/10.33619/2414-2948/97/01","pdf_url":null,"source":{"id":"https://openalex.org/S4210204670","display_name":"Bulletin of Science and Practice","issn_l":"2414-2948","issn":["2414-2948"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327988828","host_organization_name":"Publishing Center Science and Practice","host_organization_lineage":["https://openalex.org/P4327988828"],"host_organization_lineage_names":["Publishing Center Science and Practice"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Science and Practice","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.33619/2414-2948/97/01","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018582643","display_name":"Kurmanbek Sarmanovich Alybaev","orcid":"https://orcid.org/0000-0002-7962-534X","observed_orcids":["https://orcid.org/0000-0002-7962-534X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Alybaev","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7962-534X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5093496703","display_name":"Mairamgul Nurmatova","orcid":"https://orcid.org/0009-0003-4082-1161","observed_orcids":["https://orcid.org/0009-0003-4082-1161"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Nurmatova","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0003-4082-1161","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3361,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75220969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"12","first_page":"12","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.00039999998989515007,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"singular perturbation","score":0.9639999866485596},{"id":"https://openalex.org/keywords/slow-fast-systems","display_name":"singularly perturbed systems","score":0.8399999737739563},{"id":"https://openalex.org/keywords/complex-conjugate-eigenvalues","display_name":"complex conjugate eigenvalues","score":0.8009999990463257},{"id":"https://openalex.org/keywords/stability-of-equilibrium","display_name":"equilibrium stability","score":0.7720000147819519},{"id":"https://openalex.org/keywords/slow-variables","display_name":"slow variables","score":0.6600000262260437},{"id":"https://openalex.org/keywords/autonomous-systems","display_name":"autonomous systems","score":0.3790000081062317}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.8298356533050537},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.7032777070999146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6387851238250732},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6067947745323181},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.6030128598213196},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5868734121322632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5401251912117004},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.48843637108802795},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4539496898651123},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41146230697631836},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26064223051071167},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23280611634254456},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.23127037286758423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08781790733337402},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06417441368103027},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06250742077827454},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.33619/2414-2948/97/01","doi":"https://doi.org/10.33619/2414-2948/97/01","is_oa":true,"landing_page_url":"https://doi.org/10.33619/2414-2948/97/01","pdf_url":null,"source":{"id":"https://openalex.org/S4210204670","display_name":"Bulletin of Science and Practice","issn_l":"2414-2948","issn":["2414-2948"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327988828","host_organization_name":"Publishing Center Science and Practice","host_organization_lineage":["https://openalex.org/P4327988828"],"host_organization_lineage_names":["Publishing Center Science and Practice"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Science and Practice","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.33619/2414-2948/97/01","doi":"https://doi.org/10.33619/2414-2948/97/01","is_oa":true,"landing_page_url":"https://doi.org/10.33619/2414-2948/97/01","pdf_url":null,"source":{"id":"https://openalex.org/S4210204670","display_name":"Bulletin of Science and Practice","issn_l":"2414-2948","issn":["2414-2948"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327988828","host_organization_name":"Publishing Center Science and Practice","host_organization_lineage":["https://openalex.org/P4327988828"],"host_organization_lineage_names":["Publishing Center Science and Practice"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Science and Practice","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2910220530"],"related_works":["https://openalex.org/W4400815226","https://openalex.org/W4396914401","https://openalex.org/W2903193820","https://openalex.org/W2023189967","https://openalex.org/W7128920644","https://openalex.org/W7222164598","https://openalex.org/W7136035036","https://openalex.org/W7149980624","https://openalex.org/W105333815","https://openalex.org/W4403237749"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"an":[3,37],"autonomous":[4],"system":[5,35],"of":[6,10,14,21,43,53,63,74,83,89,92,94,97,99],"singularly":[7],"perturbed":[8],"equations":[9,17],"fast":[11],"variables,":[12],"consisting":[13],"four":[15],"first-order":[16],"and":[18,40],"one":[19,81],"equation":[20],"a":[22,50],"slow":[23,55],"variable.":[24,56],"The":[25,34,87],"first":[26],"approximation":[27],"matrix":[28],"has":[29,36,103],"pairwise":[30],"complex":[31,84],"conjugate":[32,85],"eigenfunctions.":[33,86],"equilibrium":[38,45,76,101],"position,":[39],"the":[41,44,54,60,72,75,90,95,100],"stability":[42,73,98],"position":[46,77,102],"is":[47,78],"lost":[48,79],"at":[49],"certain":[51],"value":[52],"At":[57],"this":[58],"point,":[59],"real":[61],"parts":[62],"all":[64],"eigenfunctions":[65],"vanish.":[66],"Early":[67],"works":[68],"considered":[69],"cases":[70],"when":[71],"by":[80],"pair":[82],"problem":[88],"phenomenon":[91],"prolongation":[93],"loss":[96],"been":[104],"solved.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2023-12-15T00:00:00"}
