{"id":"https://openalex.org/W4281769841","doi":"https://doi.org/10.1142/s0218127422500912","title":"Limit Cycles of Piecewise-Continuous Differential Systems Formed by Linear and Quadratic Isochronous Centers II","display_name":"Limit Cycles of Piecewise-Continuous Differential Systems Formed by Linear and Quadratic Isochronous Centers II","publication_year":2022,"publication_date":"2022-05-01","ids":{"openalex":"https://openalex.org/W4281769841","doi":"https://doi.org/10.1142/s0218127422500912"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422500912","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422500912","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":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/267142","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039354327","display_name":"Bilal Ghermoul","orcid":"https://orcid.org/0000-0003-0617-9665"},"institutions":[{"id":"https://openalex.org/I4210135256","display_name":"University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj","ror":"https://ror.org/03e75b898","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210135256"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Bilal Ghermoul","raw_affiliation_strings":["Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"],"raw_orcid":"https://orcid.org/0000-0003-0617-9665","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria","institution_ids":["https://openalex.org/I4210135256"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008023400","display_name":"Tayeb Salhi","orcid":"https://orcid.org/0000-0003-1220-592X"},"institutions":[{"id":"https://openalex.org/I4210135256","display_name":"University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj","ror":"https://ror.org/03e75b898","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210135256"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Tayeb Salhi","raw_affiliation_strings":["Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria","institution_ids":["https://openalex.org/I4210135256"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039354327"],"corresponding_institution_ids":["https://openalex.org/I4210135256"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13163258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"06","first_page":null,"last_page":null},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11844","display_name":"Lipid metabolism and biosynthesis","score":0.9629999995231628,"subfield":{"id":"https://openalex.org/subfields/1303","display_name":"Biochemistry"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10492","display_name":"Microtubule and mitosis dynamics","score":0.9171000123023987,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.7432751655578613},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6853644847869873},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.678691029548645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6726150512695312},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.6377912163734436},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6127874851226807},{"id":"https://openalex.org/keywords/quadratic-differential","display_name":"Quadratic differential","score":0.4661226272583008},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45643699169158936},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4284853935241699},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.336692214012146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16007909178733826}],"concepts":[{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.7432751655578613},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6853644847869873},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.678691029548645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6726150512695312},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.6377912163734436},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6127874851226807},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.4661226272583008},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45643699169158936},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4284853935241699},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.336692214012146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16007909178733826},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127422500912","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422500912","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"},{"id":"pmh:oai:ddd.uab.cat:267142","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/267142","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:267142","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/267142","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W965103837","https://openalex.org/W1992299830","https://openalex.org/W2049815318","https://openalex.org/W2182274314","https://openalex.org/W2765944944"],"related_works":["https://openalex.org/W2051439117","https://openalex.org/W4388297534","https://openalex.org/W1673883441","https://openalex.org/W3195693990","https://openalex.org/W4298109871","https://openalex.org/W2765944944","https://openalex.org/W2313188567","https://openalex.org/W4248124207","https://openalex.org/W4226164715","https://openalex.org/W3096660584"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,10,17,27,54,78],"crossing":[3,82,94],"periodic":[4],"orbits":[5],"and":[6,42,87],"limit":[7,83,95],"cycles":[8,84],"of":[9,81],"planar":[11],"piecewise-continuous":[12,75],"differential":[13,76],"systems":[14,77],"separated":[15],"by":[16],"straight-line":[18],"[Formula:":[19,24,32,35,44,58,61],"see":[20,25,33,36,45,59,62],"text]":[21,26,37,46,63],"having":[22,92],"in":[23,43,68],"general":[28],"quadratic":[29,49,55],"isochronous":[30,50,56],"center":[31,51,57],"text],":[34,60],"after":[38],"an":[39,47],"affine":[40],"transformation,":[41],"arbitrary":[48],"except":[52],"for":[53],"which":[64],"has":[65],"been":[66],"studied":[67],"[Ghermoul":[69],"et":[70],"al.,":[71],"2021].":[72],"For":[73],"these":[74],"upper":[79],"bound":[80],"is":[85],"2,":[86],"there":[88],"are":[89],"specific":[90],"examples":[91],"one":[93],"cycle.":[96]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
