{"id":"https://openalex.org/W3211989293","doi":"https://doi.org/10.22075/ijnaa.2021.23049.2468","title":"On the maximum number of limit cycles of a planar differential system","display_name":"On the maximum number of limit cycles of a planar differential system","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W3211989293","doi":"https://doi.org/10.22075/ijnaa.2021.23049.2468","mag":"3211989293"},"language":"en","primary_location":{"id":"mag:3211989293","doi":"https://doi.org/10.22075/ijnaa.2021.23049.2468","is_oa":false,"landing_page_url":"https://ijnaa.semnan.ac.ir/article_5760_8a9b3bf64826dfec536fc0f11d6a15d0.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764873337","display_name":"International journal of nonlinear analysis and applications","issn_l":"2008-6822","issn":["2008-6822"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International journal of nonlinear analysis and applications","raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5085526668","display_name":"Sana Karfes","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I108754898","display_name":"Badji Mokhtar-Annaba University","ror":"https://ror.org/03sf55932","country_code":"DZ","type":"education","lineage":["https://openalex.org/I108754898"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Sana Karfes","raw_affiliation_strings":["Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria","institution_ids":["https://openalex.org/I108754898"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017756911","display_name":"Elbahi Hadidi","orcid":"https://orcid.org/0000-0002-2200-4729","observed_orcids":["https://orcid.org/0000-0002-2200-4729"]},"institutions":[{"id":"https://openalex.org/I108754898","display_name":"Badji Mokhtar-Annaba University","ror":"https://ror.org/03sf55932","country_code":"DZ","type":"education","lineage":["https://openalex.org/I108754898"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Elbahi Hadidi","raw_affiliation_strings":["Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria","institution_ids":["https://openalex.org/I108754898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064460601","display_name":"Mohamed Amine Kerker","orcid":"https://orcid.org/0000-0003-2215-533X","observed_orcids":["https://orcid.org/0000-0003-2215-533X"]},"institutions":[{"id":"https://openalex.org/I108754898","display_name":"Badji Mokhtar-Annaba University","ror":"https://ror.org/03sf55932","country_code":"DZ","type":"education","lineage":["https://openalex.org/I108754898"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mohamed Amine Kerker","raw_affiliation_strings":["Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria","institution_ids":["https://openalex.org/I108754898"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I108754898"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04171705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"1","first_page":"1462","last_page":"1478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9990000128746033,"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":0.00019999999494757503,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/limit-cycles","display_name":"limit cycles","score":0.9990000128746033},{"id":"https://openalex.org/keywords/planar-differential-systems","display_name":"planar differential systems","score":0.8109999895095825},{"id":"https://openalex.org/keywords/perturbed-systems","display_name":"perturbed systems","score":0.6710000038146973},{"id":"https://openalex.org/keywords/averaging-theory","display_name":"averaging theory","score":0.7310000061988831},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.46299999952316284},{"id":"https://openalex.org/keywords/polynomial-perturbations","display_name":"polynomial perturbations","score":0.8159999847412109},{"id":"https://openalex.org/keywords/small-parameter","display_name":"small parameter","score":0.3709999918937683}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7684028744697571},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7316412925720215},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6798532605171204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6148674488067627},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6144979000091553},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6134909391403198},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5814599990844727},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5704659223556519},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5363048315048218},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46881747245788574},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.44040393829345703},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.42375028133392334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37744075059890747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34257668256759644},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3282736837863922},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20275580883026123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05887654423713684},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3211989293","doi":"https://doi.org/10.22075/ijnaa.2021.23049.2468","is_oa":false,"landing_page_url":"https://ijnaa.semnan.ac.ir/article_5760_8a9b3bf64826dfec536fc0f11d6a15d0.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2764873337","display_name":"International journal of nonlinear analysis and applications","issn_l":"2008-6822","issn":["2008-6822"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International journal of nonlinear analysis and applications","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4398161092","https://openalex.org/W4210670722","https://openalex.org/W2889091344","https://openalex.org/W7220594646","https://openalex.org/W4299367093","https://openalex.org/W3183381249","https://openalex.org/W7110565397","https://openalex.org/W4409094758","https://openalex.org/W2295186892","https://openalex.org/W3214898863"],"abstract_inverted_index":{"In":[0,65],"this":[1],"work,":[2],"we":[3,68],"are":[4],"interested":[5],"in":[6],"the":[7,10,49,66,74],"study":[8],"of":[9,13,45,52,62],"limit":[11,63],"cycles":[12],"a\u00a0perturbed":[14],"differential":[15],"system":[16],"in\u00a0":[17],"(mathbb{R}^2),":[18],"given":[19],"as":[20],"follows[left{begin{array}{l}dot{x}=y,":[21],"\\dot{y}=-x-varepsilon":[22],"(1+sin":[23],"^{m}(theta":[24],"))psi":[25],"(x,y),%end{array}%right.]where":[26],"(varepsilon)":[27],"is":[28,32,41],"small":[29],"enough,":[30],"(m)":[31],"a":[33,42],"non-negative":[34],"integer,":[35],"(tan\u00a0(theta":[36],")=y/x),":[37],"and":[38],"(psi":[39],"(x,y))":[40],"real":[43],"polynomial":[44],"degree":[46],"(ngeq1).":[47],"We\u00a0use":[48],"averaging":[50],"theory":[51],"first-order":[53],"to":[54,72],"provide":[55],"an":[56],"upper":[57],"bound":[58],"for":[59],"the\u00a0maximum":[60],"number":[61],"cycles.":[64],"end,":[67],"present":[69],"some":[70],"numerical\u00a0examples":[71],"illustrate":[73],"theoretical":[75],"results.":[76]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2021-11-22T00:00:00"}
