{"id":"https://openalex.org/W2473667848","doi":"https://doi.org/10.1142/s0218127416300159","title":"Periodic and Chaotic Dynamics of the Ehrhard\u2013M\u00fcller System","display_name":"Periodic and Chaotic Dynamics of the Ehrhard\u2013M\u00fcller System","publication_year":2016,"publication_date":"2016-06-15","ids":{"openalex":"https://openalex.org/W2473667848","doi":"https://doi.org/10.1142/s0218127416300159","mag":"2473667848"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416300159","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416300159","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/A5100667205","display_name":"Junho Park","orcid":"https://orcid.org/0000-0001-5947-0064"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Junho Park","raw_affiliation_strings":["School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090660509","display_name":"Hyunho Lee","orcid":"https://orcid.org/0000-0002-7772-5400"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyunho Lee","raw_affiliation_strings":["School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091044064","display_name":"Jong\u2010Jin Baik","orcid":"https://orcid.org/0000-0003-3709-0532"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jong-Jin Baik","raw_affiliation_strings":["School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100667205"],"corresponding_institution_ids":["https://openalex.org/I139264467"],"apc_list":null,"apc_paid":null,"fwci":0.9044,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75793589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"06","first_page":"1630015","last_page":"1630015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9948999881744385,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/chaotic","display_name":"Chaotic","score":0.8072646856307983},{"id":"https://openalex.org/keywords/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.6106899380683899},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5747777819633484},{"id":"https://openalex.org/keywords/chaotic-mixing","display_name":"Chaotic mixing","score":0.5395317673683167},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5263294577598572},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5262005925178528},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5020096302032471},{"id":"https://openalex.org/keywords/crisis","display_name":"Crisis","score":0.4557378888130188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4401002824306488},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.43662065267562866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37147635221481323},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36955103278160095},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.36350393295288086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36018502712249756},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.2968515157699585},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.2756009101867676},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.2175125777721405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09541195631027222}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.8072646856307983},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.6106899380683899},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5747777819633484},{"id":"https://openalex.org/C131436191","wikidata":"https://www.wikidata.org/wiki/Q5072842","display_name":"Chaotic mixing","level":3,"score":0.5395317673683167},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5263294577598572},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5262005925178528},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5020096302032471},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.4557378888130188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4401002824306488},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.43662065267562866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37147635221481323},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36955103278160095},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.36350393295288086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36018502712249756},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.2968515157699585},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.2756009101867676},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2175125777721405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09541195631027222},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416300159","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416300159","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/G1473619855","display_name":null,"funder_award_id":"KMIPA2015-5100","funder_id":"https://openalex.org/F4320322036","funder_display_name":"Korea Meteorological Administration"}],"funders":[{"id":"https://openalex.org/F4320322036","display_name":"Korea Meteorological Administration","ror":"https://ror.org/04nrmrg07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W122882714","https://openalex.org/W1970824991","https://openalex.org/W1980755872","https://openalex.org/W1986322491","https://openalex.org/W1988855581","https://openalex.org/W1990774783","https://openalex.org/W1995195789","https://openalex.org/W1997041501","https://openalex.org/W1997536107","https://openalex.org/W2012923551","https://openalex.org/W2015639518","https://openalex.org/W2062266080","https://openalex.org/W2070655649","https://openalex.org/W2075019393","https://openalex.org/W2080670027","https://openalex.org/W2082407103","https://openalex.org/W2083340044","https://openalex.org/W2087136490","https://openalex.org/W2089997475","https://openalex.org/W2092961463","https://openalex.org/W2096668061","https://openalex.org/W2131928612","https://openalex.org/W2141394518","https://openalex.org/W2152345328","https://openalex.org/W3093361922","https://openalex.org/W3098807575","https://openalex.org/W3100115818"],"related_works":["https://openalex.org/W2059902367","https://openalex.org/W2354020126","https://openalex.org/W2029968665","https://openalex.org/W2133000644","https://openalex.org/W4310689763","https://openalex.org/W2022042062","https://openalex.org/W4321770257","https://openalex.org/W2148448414","https://openalex.org/W2949689666","https://openalex.org/W2473667848"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"nonlinear":[3],"ordinary":[4],"differential":[5],"equations":[6,35],"of":[7,22,28,33,47,50],"the":[8,20,34,39,63,67,76,93,96],"Ehrhard\u2013M\u00fcller":[9],"system":[10],"which":[11],"describes":[12],"natural":[13],"convection":[14],"in":[15,19,44],"a":[16],"single-phase":[17],"loop":[18],"presence":[21],"nonsymmetric":[23],"heating.":[24],"Stability":[25],"and":[26,30,38,53,99],"dynamics":[27],"periodic":[29,52,64,97],"chaotic":[31,54,68,77],"behaviors":[32,60],"are":[36,56,72,103],"investigated":[37],"periodicity":[40],"diagram":[41],"is":[42,85],"obtained":[43,104,110],"wide":[45],"ranges":[46],"parameters.":[48],"Regimes":[49],"both":[51],"solutions":[55],"observed":[57],"with":[58,79,107],"complex":[59],"such":[61],"that":[62],"regimes":[65,98],"enclose":[66],"regime":[69,78],"while":[70],"they":[71],"also":[73],"immersed":[74],"inside":[75],"various":[80],"shapes.":[81],"An":[82],"asymptotic":[83,100],"analysis":[84],"performed":[86],"for":[87],"sufficiently":[88],"large":[89],"parameters":[90],"to":[91,105],"understand":[92],"enclosure":[94],"by":[95],"limit":[101,108],"cycles":[102,109],"compare":[106],"from":[111],"numerical":[112],"results.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}