{"id":"https://openalex.org/W2057038694","doi":"https://doi.org/10.1137/0153053","title":"New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High <i>r</i> in the Lorenz Equations","display_name":"New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High <i>r</i> in the Lorenz Equations","publication_year":1993,"publication_date":"1993-08-01","ids":{"openalex":"https://openalex.org/W2057038694","doi":"https://doi.org/10.1137/0153053","mag":"2057038694"},"language":"en","primary_location":{"id":"doi:10.1137/0153053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153053","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jibin Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100427566","display_name":"Jianming Zhang","orcid":"https://orcid.org/0000-0002-4805-5727"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianming Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9423,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.73521127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"4","first_page":"1059","last_page":"1071"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9994999766349792,"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9587163925170898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6902893781661987},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.6628766059875488},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6490532755851746},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.6163277626037598},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.59332674741745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5010466575622559},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.47630250453948975},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.43919315934181213},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.42594707012176514},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36763471364974976},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3409136235713959},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.29286661744117737},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21503442525863647},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1778777837753296},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08469796180725098},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.06470957398414612}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9587163925170898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6902893781661987},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.6628766059875488},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6490532755851746},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.6163277626037598},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.59332674741745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5010466575622559},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.47630250453948975},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.43919315934181213},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.42594707012176514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36763471364974976},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3409136235713959},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.29286661744117737},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21503442525863647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1778777837753296},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08469796180725098},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.06470957398414612},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0153053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153053","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1573927207","https://openalex.org/W1967878976","https://openalex.org/W1989097268","https://openalex.org/W2038397330","https://openalex.org/W2039419724","https://openalex.org/W2055737217","https://openalex.org/W2069185213","https://openalex.org/W2091651221","https://openalex.org/W2128949314","https://openalex.org/W3173176713","https://openalex.org/W4229672964","https://openalex.org/W4231102510","https://openalex.org/W4293079168"],"related_works":["https://openalex.org/W2890492950","https://openalex.org/W3115184012","https://openalex.org/W1984913125","https://openalex.org/W2096327469","https://openalex.org/W2767051478","https://openalex.org/W2955054485","https://openalex.org/W2032911812","https://openalex.org/W2147240237","https://openalex.org/W2481001085","https://openalex.org/W1984417388"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,12,25,36,42],"existence":[4],"of":[5,44],"periodic":[6],"solutions":[7],"and":[8],"homoclinic":[9],"orbits":[10],"in":[11],"Lorenz":[13,26],"equations":[14],"with":[15,24],"high":[16],"r":[17],"is":[18],"rigorously":[19],"proved.":[20],"The":[21],"paper":[22],"deals":[23],"model":[27],"as":[28],"a":[29],"three-dimensional":[30,37],"perturbed":[31],"Hamiltonian":[32],"system":[33],"generated":[34],"by":[35],"Lie":[38],"algebra.":[39],"By":[40],"using":[41],"method":[43],"Melnikov":[45],"vector,the":[46],"explicit":[47],"parametric":[48],"conditions":[49],"can":[50],"be":[51],"determined.":[52]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}