{"id":"https://openalex.org/W2913111680","doi":"https://doi.org/10.1142/s0218127419500032","title":"Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs","display_name":"Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2913111680","doi":"https://doi.org/10.1142/s0218127419500032","mag":"2913111680"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419500032","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500032","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023318948","display_name":"Yusen Wu","orcid":"https://orcid.org/0000-0003-3975-6828"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yusen Wu","raw_affiliation_strings":["School of Statistics, Qufu Normal University, Shandong, Qufu 273165, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Statistics, Qufu Normal University, Shandong, Qufu 273165, P. R. China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100325327","display_name":"Hongwei Li","orcid":"https://orcid.org/0000-0001-9461-4668"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongwei Li","raw_affiliation_strings":["School of Mathematics and Statistics, Linyi University, Shandong, Linyi 276005, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Linyi University, Shandong, Linyi 276005, P. R. China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108681726","display_name":"Ahmed Alsaedi","orcid":"https://orcid.org/0000-0003-3452-8922"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmed Alsaedi","raw_affiliation_strings":["Nonlinear Analysis and Applied Mathematics (NAAM), Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics (NAAM), Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100325327"],"corresponding_institution_ids":["https://openalex.org/I15823474"],"apc_list":null,"apc_paid":null,"fwci":0.3799,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53481793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"29","issue":"01","first_page":"1950003","last_page":"1950003"},"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":1.0,"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":1.0,"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":0.9653000235557556,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9300000071525574,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8162429332733154},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7585577964782715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7520058155059814},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6737838983535767},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.6507081389427185},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6200032234191895},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5859153866767883},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.572202742099762},{"id":"https://openalex.org/keywords/singular-point-of-a-curve","display_name":"Singular point of a curve","score":0.49612292647361755},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4793066084384918},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47870567440986633},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4786421060562134},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4652588963508606},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45078954100608826},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4487876892089844},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4262658655643463},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.4243202209472656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42300012707710266},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18702247738838196},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13421937823295593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1334179937839508},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08363807201385498}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8162429332733154},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7585577964782715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7520058155059814},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6737838983535767},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.6507081389427185},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6200032234191895},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5859153866767883},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.572202742099762},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.49612292647361755},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4793066084384918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47870567440986633},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4786421060562134},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4652588963508606},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45078954100608826},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4487876892089844},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4262658655643463},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.4243202209472656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42300012707710266},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18702247738838196},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13421937823295593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1334179937839508},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08363807201385498},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127419500032","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500032","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3227581914","display_name":null,"funder_award_id":"11101126","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W17819749","https://openalex.org/W589366791","https://openalex.org/W1181435521","https://openalex.org/W1971377732","https://openalex.org/W1983540230","https://openalex.org/W1996316100","https://openalex.org/W1998747042","https://openalex.org/W2001044557","https://openalex.org/W2001070781","https://openalex.org/W2001626398","https://openalex.org/W2006732470","https://openalex.org/W2026026372","https://openalex.org/W2028888525","https://openalex.org/W2038411646","https://openalex.org/W2048719985","https://openalex.org/W2053496265","https://openalex.org/W2055439733","https://openalex.org/W2056447802","https://openalex.org/W2063451147","https://openalex.org/W2071586795","https://openalex.org/W2076924905","https://openalex.org/W2079830378","https://openalex.org/W2086054590","https://openalex.org/W2089595622","https://openalex.org/W2090352524","https://openalex.org/W2092620540","https://openalex.org/W2100430328","https://openalex.org/W2129875234","https://openalex.org/W2166490084","https://openalex.org/W2291077683","https://openalex.org/W2306799711","https://openalex.org/W2402851073","https://openalex.org/W2726863439","https://openalex.org/W2745623429","https://openalex.org/W2774033034","https://openalex.org/W2783637007","https://openalex.org/W2808834761","https://openalex.org/W2810279415","https://openalex.org/W2810428220","https://openalex.org/W4229944874"],"related_works":["https://openalex.org/W4281733204","https://openalex.org/W2151569234","https://openalex.org/W1880931252","https://openalex.org/W2369348556","https://openalex.org/W2340824690","https://openalex.org/W2134241853","https://openalex.org/W2059366144","https://openalex.org/W621647875","https://openalex.org/W2014560721","https://openalex.org/W1993945523"],"abstract_inverted_index":{"In":[0],"this":[1,23,67],"paper,":[2],"a":[3,13,58],"class":[4,59],"of":[5,11,15,25,30,39,48,57,60],"second-order":[6,31],"ODEs":[7,32],"is":[8,20],"investigated.":[9],"First":[10],"all,":[12,54],"method":[14],"computing":[16],"singular":[17],"point":[18],"values":[19],"established":[21],"for":[22],"kind":[24],"systems.":[26],"Then,":[27],"two":[28],"classes":[29],"are":[33,51,63],"studied":[34],"to":[35],"illustrate":[36],"the":[37,40,43],"efficiency":[38],"method,":[41],"and":[42,46],"center":[44,55],"conditions":[45,56],"bifurcation":[47],"limit":[49],"cycles":[50],"obtained.":[52],"Above":[53],"non-polynomial":[61],"systems":[62],"classified":[64],"by":[65],"using":[66],"method.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}