{"id":"https://openalex.org/W3039243050","doi":"https://doi.org/10.1142/s0218127420300177","title":"Bifurcation Analysis in Planar Quadratic Differential Systems with Boundary","display_name":"Bifurcation Analysis in Planar Quadratic Differential Systems with Boundary","publication_year":2020,"publication_date":"2020-06-15","ids":{"openalex":"https://openalex.org/W3039243050","doi":"https://doi.org/10.1142/s0218127420300177","mag":"3039243050"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420300177","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420300177","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/A5049433846","display_name":"Jocelyn A. Castro","orcid":"https://orcid.org/0000-0003-4237-170X"},"institutions":[{"id":"https://openalex.org/I4061448","display_name":"Universidad de Sonora","ror":"https://ror.org/00c32gy34","country_code":"MX","type":"education","lineage":["https://openalex.org/I4061448"]},{"id":"https://openalex.org/I98461037","display_name":"Tecnol\u00f3gico de Monterrey","ror":"https://ror.org/03ayjn504","country_code":"MX","type":"education","lineage":["https://openalex.org/I98461037"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jocelyn A. Castro","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Sonora, Hermosillo, Sonora 83000, M\u00e9xico","Instituto Tecnol\u00f3gico y de Estudios Superiores de Monterrey, Sonora Norte 83000, M\u00e9xico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Sonora, Hermosillo, Sonora 83000, M\u00e9xico","institution_ids":["https://openalex.org/I4061448"]},{"raw_affiliation_string":"Instituto Tecnol\u00f3gico y de Estudios Superiores de Monterrey, Sonora Norte 83000, M\u00e9xico","institution_ids":["https://openalex.org/I98461037"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021373250","display_name":"Fernando Verduzco","orcid":"https://orcid.org/0000-0002-3237-2090"},"institutions":[{"id":"https://openalex.org/I4061448","display_name":"Universidad de Sonora","ror":"https://ror.org/00c32gy34","country_code":"MX","type":"education","lineage":["https://openalex.org/I4061448"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Fernando Verduzco","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Sonora, Hermosillo, Sonora 83000, M\u00e9xico"],"raw_orcid":"https://orcid.org/0000-0002-3237-2090","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Sonora, Hermosillo, Sonora 83000, M\u00e9xico","institution_ids":["https://openalex.org/I4061448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16917785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"07","first_page":"2030017","last_page":"2030017"},"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":0.9998999834060669,"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":0.9998999834060669,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8040422201156616},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.7214542627334595},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.7060879468917847},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6843169331550598},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.6646260023117065},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5575336217880249},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5453627705574036},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5372891426086426},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5294850468635559},{"id":"https://openalex.org/keywords/quadratic-differential","display_name":"Quadratic differential","score":0.46569928526878357},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.4606952369213104},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42768943309783936},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4144755005836487},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16005778312683105},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13266316056251526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0874963104724884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8040422201156616},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.7214542627334595},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.7060879468917847},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6843169331550598},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.6646260023117065},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5575336217880249},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5453627705574036},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5372891426086426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5294850468635559},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.46569928526878357},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.4606952369213104},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42768943309783936},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4144755005836487},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16005778312683105},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13266316056251526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0874963104724884},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420300177","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420300177","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":[],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1576847343","https://openalex.org/W1603340857","https://openalex.org/W1977907719","https://openalex.org/W2047449028","https://openalex.org/W2089466166","https://openalex.org/W2089876099","https://openalex.org/W2471371264","https://openalex.org/W2754851260","https://openalex.org/W4298421983"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2775656422","https://openalex.org/W3020506472","https://openalex.org/W4245057904","https://openalex.org/W2025138898","https://openalex.org/W4281733204","https://openalex.org/W4366091759","https://openalex.org/W2978098199","https://openalex.org/W2369348556","https://openalex.org/W2078078632"],"abstract_inverted_index":{"Given":[0],"a":[1,8,44,61],"planar":[2],"quadratic":[3,48],"differential":[4,49],"system":[5],"delimited":[6],"by":[7,77,92],"straight":[9],"line,":[10],"we":[11,42,59,69,108],"are":[12,32,140],"interested":[13],"in":[14],"studying":[15],"the":[16,23,26,78,88,93,105,113,124,127,130,138],"bifurcation":[17,134],"phenomena":[18],"that":[19],"can":[20],"arise":[21],"when":[22],"position":[24],"on":[25],"boundary":[27,101],"of":[28,36,47,74,80,84,95,115,129],"two":[29,71,81,143],"tangency":[30,55],"points":[31,83],"considered":[33],"as":[34],"parameters":[35],"bifurcation.":[37],"First,":[38],"under":[39],"generic":[40],"conditions,":[41],"find":[43,60,109],"two-parametric":[45],"family":[46],"systems":[50],"with":[51,142],"at":[52],"least":[53],"one":[54,73,96,100],"point.":[56,103],"After":[57],"that,":[58],"normal":[62],"form":[63],"for":[64,112,123],"this":[65],"parameterized":[66],"family.":[67],"Next,":[68],"study":[70],"subfamilies,":[72],"them":[75],"characterized":[76,91],"existence":[79,94,114,128],"fold":[82,97],"different":[85],"nature,":[86],"and":[87,99,120],"other":[89],"one,":[90],"point":[98],"equilibrium":[102],"For":[104],"first":[106],"family,":[107,126],"sufficient":[110],"conditions":[111],"stationary":[116],"bifurcations:":[117],"saddle-node,":[118],"transcritical":[119,132],"pitchfork,":[121],"while":[122],"second":[125],"called":[131],"Bogdanov\u2013Takens":[133],"is":[135],"proved.":[136],"Finally,":[137],"results":[139],"illustrated":[141],"examples.":[144]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}