{"id":"https://openalex.org/W2624493067","doi":"https://doi.org/10.1142/s0218127417500808","title":"Bifurcations and Exact Solutions of the Equation of Barotropic FRW Cosmologies","display_name":"Bifurcations and Exact Solutions of the Equation of Barotropic FRW Cosmologies","publication_year":2017,"publication_date":"2017-05-01","ids":{"openalex":"https://openalex.org/W2624493067","doi":"https://doi.org/10.1142/s0218127417500808","mag":"2624493067"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417500808","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500808","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/A5100599691","display_name":"Jibin Li","orcid":"https://orcid.org/0000-0003-4839-5956"},"institutions":[{"id":"https://openalex.org/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]},{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jibin Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086628608","display_name":"Tonghua Zhang","orcid":"https://orcid.org/0000-0003-0510-1428"},"institutions":[{"id":"https://openalex.org/I57093077","display_name":"Swinburne University of Technology","ror":"https://ror.org/031rekg67","country_code":"AU","type":"education","lineage":["https://openalex.org/I57093077"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Tonghua Zhang","raw_affiliation_strings":["Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia","institution_ids":["https://openalex.org/I57093077"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4879,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70914229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"05","first_page":"1750080","last_page":"1750080"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/barotropic-fluid","display_name":"Barotropic fluid","score":0.8994796276092529},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.8417513370513916},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.8250327110290527},{"id":"https://openalex.org/keywords/friedmann\u2013lema\u00eetre\u2013robertson\u2013walker-metric","display_name":"Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker metric","score":0.6817528009414673},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6708911061286926},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6322422623634338},{"id":"https://openalex.org/keywords/peakon","display_name":"Peakon","score":0.5436837077140808},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5060431361198425},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4871077537536621},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48152002692222595},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.4465835690498352},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4371626079082489},{"id":"https://openalex.org/keywords/homothetic-transformation","display_name":"Homothetic transformation","score":0.4343389868736267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36527514457702637},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.34575605392456055},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.32681822776794434},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.2882812023162842},{"id":"https://openalex.org/keywords/cosmology","display_name":"Cosmology","score":0.14036783576011658},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10077202320098877},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09822720289230347},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0952196717262268},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.09224054217338562}],"concepts":[{"id":"https://openalex.org/C29712183","wikidata":"https://www.wikidata.org/wiki/Q739293","display_name":"Barotropic fluid","level":2,"score":0.8994796276092529},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8417513370513916},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.8250327110290527},{"id":"https://openalex.org/C30864177","wikidata":"https://www.wikidata.org/wiki/Q742982","display_name":"Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker metric","level":3,"score":0.6817528009414673},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6708911061286926},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6322422623634338},{"id":"https://openalex.org/C155091195","wikidata":"https://www.wikidata.org/wiki/Q7157892","display_name":"Peakon","level":3,"score":0.5436837077140808},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5060431361198425},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4871077537536621},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48152002692222595},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.4465835690498352},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4371626079082489},{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.4343389868736267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36527514457702637},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.34575605392456055},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32681822776794434},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.2882812023162842},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.14036783576011658},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10077202320098877},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09822720289230347},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0952196717262268},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.09224054217338562},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127417500808","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500808","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:researchbank.swinburne.edu.au:c438264b-9985-4ab2-881a-0222f500eeab/1","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.3/437394","pdf_url":null,"source":{"id":"https://openalex.org/S4306401157","display_name":"Swinburne Research Bank (Swinburne University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I57093077","host_organization_name":"Swinburne University of Technology","host_organization_lineage":["https://openalex.org/I57093077"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 27, no. 5 (May 2017), article no. 5","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1716058852","https://openalex.org/W1970680427","https://openalex.org/W1994828676","https://openalex.org/W2027708627","https://openalex.org/W2052528969","https://openalex.org/W2068577046","https://openalex.org/W2114463065","https://openalex.org/W4289981527"],"related_works":["https://openalex.org/W2084665907","https://openalex.org/W2053879682","https://openalex.org/W1998618626","https://openalex.org/W2523749156","https://openalex.org/W2029939732","https://openalex.org/W3019927421","https://openalex.org/W3123020351","https://openalex.org/W2030202422","https://openalex.org/W4283730124","https://openalex.org/W2754726100"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,18,36],"study":[4],"the":[5,13,22,26],"equation":[6],"of":[7,15,21,25,42],"barotropic":[8],"Friedmann\u2013Robertson\u2013Walker":[9],"cosmologies.":[10],"By":[11],"using":[12],"method":[14],"dynamical":[16,29],"systems,":[17],"obtain":[19],"bifurcations":[20],"phase":[23],"portraits":[24],"corresponding":[27],"planar":[28],"system.":[30],"Corresponding":[31],"to":[32],"different":[33],"level":[34],"curves,":[35],"derive":[37],"exact":[38],"explicit":[39],"parametric":[40],"representations":[41],"bounded":[43],"and":[44,55,58],"unbounded":[45],"solutions,":[46,50,53],"such":[47],"as":[48],"periodic":[49,51],"peakon":[52],"homoclinic":[54],"heteroclinic":[56],"solutions":[57],"compacton":[59],"solutions.":[60]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}