{"id":"https://openalex.org/W2990569851","doi":"https://doi.org/10.1142/s0218127419300349","title":"Multistability and Bubbling Route to Chaos in a Deterministic Model for Geomagnetic Field Reversals","display_name":"Multistability and Bubbling Route to Chaos in a Deterministic Model for Geomagnetic Field Reversals","publication_year":2019,"publication_date":"2019-11-01","ids":{"openalex":"https://openalex.org/W2990569851","doi":"https://doi.org/10.1142/s0218127419300349","mag":"2990569851"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419300349","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419300349","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":true,"oa_status":"green","oa_url":"https://repositorio.udesc.br/handle/UDESC/5212","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077221436","display_name":"Paulo C. Rech","orcid":"https://orcid.org/0000-0003-2235-0469"},"institutions":[{"id":"https://openalex.org/I164790352","display_name":"Universidade do Estado de Santa Catarina","ror":"https://ror.org/03ztsbk67","country_code":"BR","type":"education","lineage":["https://openalex.org/I164790352"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Paulo C. Rech","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil","institution_ids":["https://openalex.org/I164790352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077412142","display_name":"Sudarshan Dhua","orcid":"https://orcid.org/0000-0001-6973-7463"},"institutions":[{"id":"https://openalex.org/I4210153924","display_name":"National Institute of Technology Andhra Pradesh","ror":"https://ror.org/0456pcg54","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210153924"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sudarshan Dhua","raw_affiliation_strings":["School of Sciences, National Institute of Technology, Andhra Pradesh-534102, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences, National Institute of Technology, Andhra Pradesh-534102, India","institution_ids":["https://openalex.org/I4210153924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057755539","display_name":"N. C. Pati","orcid":"https://orcid.org/0000-0001-9906-5557"},"institutions":[{"id":"https://openalex.org/I132359460","display_name":"University of Burdwan","ror":"https://ror.org/05cyd8v32","country_code":"IN","type":"education","lineage":["https://openalex.org/I132359460"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"N. C. Pati","raw_affiliation_strings":["Department of Mathematics, The University of Burdwan, Burdwan-713104, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0001-9906-5557","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Burdwan, Burdwan-713104, West Bengal, India","institution_ids":["https://openalex.org/I132359460"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077221436"],"corresponding_institution_ids":["https://openalex.org/I164790352"],"apc_list":null,"apc_paid":null,"fwci":0.5763,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.67106508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"29","issue":"12","first_page":"1930034","last_page":"1930034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7879112958908081},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.7666055560112},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.7664822936058044},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7305266857147217},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6884555220603943},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6352193355560303},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5850578546524048},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5181933045387268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49223437905311584},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.4758695960044861},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.4612821936607361},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4484545886516571},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.44055435061454773},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.3673405647277832},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36497336626052856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3462008237838745},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.22015425562858582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1320158839225769},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08726540207862854}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7879112958908081},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.7666055560112},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7664822936058044},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7305266857147217},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6884555220603943},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6352193355560303},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5850578546524048},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5181933045387268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49223437905311584},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.4758695960044861},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.4612821936607361},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4484545886516571},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.44055435061454773},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.3673405647277832},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36497336626052856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3462008237838745},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.22015425562858582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1320158839225769},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08726540207862854},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127419300349","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419300349","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:repositorio.udesc.br:UDESC/5212","is_oa":true,"landing_page_url":"https://repositorio.udesc.br/handle/UDESC/5212","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UDESC","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.udesc.br:UDESC/5212","is_oa":true,"landing_page_url":"https://repositorio.udesc.br/handle/UDESC/5212","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UDESC","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1577466517","https://openalex.org/W1899958445","https://openalex.org/W1966854094","https://openalex.org/W1984072046","https://openalex.org/W1987872178","https://openalex.org/W1996728098","https://openalex.org/W2000080571","https://openalex.org/W2003304048","https://openalex.org/W2024308405","https://openalex.org/W2051008133","https://openalex.org/W2062154188","https://openalex.org/W2069436097","https://openalex.org/W2070482276","https://openalex.org/W2070502248","https://openalex.org/W2072426572","https://openalex.org/W2072549489","https://openalex.org/W2093182255","https://openalex.org/W2094343138","https://openalex.org/W2141394518","https://openalex.org/W2143811734","https://openalex.org/W2152254020","https://openalex.org/W2168711358","https://openalex.org/W2341495304","https://openalex.org/W2588148365","https://openalex.org/W2714899197","https://openalex.org/W2740752871","https://openalex.org/W2794916323","https://openalex.org/W2801680959","https://openalex.org/W2903779703","https://openalex.org/W2911469887","https://openalex.org/W3103949472"],"related_works":["https://openalex.org/W2788936494","https://openalex.org/W3186859053","https://openalex.org/W2058823188","https://openalex.org/W2970483356","https://openalex.org/W2009540600","https://openalex.org/W4285227026","https://openalex.org/W3043043274","https://openalex.org/W2979506885","https://openalex.org/W2386717867","https://openalex.org/W2990569851"],"abstract_inverted_index":{"We":[0],"report":[1],"coexisting":[2],"multiple":[3],"attractors":[4],"and":[5,84,129],"birth":[6],"of":[7,15,25,40,72,86,97,115,131],"chaos":[8],"via":[9],"period-bubbling":[10],"cascades":[11,88],"in":[12],"a":[13,23,68,77,100],"model":[14,20],"geomagnetic":[16],"field":[17],"reversals.":[18],"The":[19,111],"system":[21,117],"comprises":[22],"set":[24],"three":[26,33],"coupled":[27],"first-order":[28],"quadratic":[29],"nonlinear":[30,73],"equations":[31],"with":[32],"control":[34],"parameters.":[35],"Up":[36],"to":[37,82],"seven":[38],"kinds":[39],"multistable":[41],"attractors,":[42],"viz.":[43],"fixed":[44,46,51,53],"point-periodic,":[45],"point-chaotic,":[47],"periodic\u2013periodic,":[48],"periodic-chaotic,":[49],"chaotic\u2013chaotic,":[50],"point-periodic\u2013periodic,":[52],"point-periodic-chaotic":[54],"are":[55,118],"obtained":[56],"depending":[57],"on":[58],"the":[59,93,98,116],"initial":[60],"conditions":[61],"for":[62],"critical":[63,101],"parameter":[64],"sets.":[65],"Antimonotonicity":[66],"is":[67,89,104],"striking":[69],"characteristic":[70],"feature":[71],"systems":[74],"through":[75],"which":[76],"full":[78],"Feigenbaum":[79],"tree":[80],"corresponding":[81],"creation":[83],"annihilation":[85],"period-doubling":[87],"developed.":[90],"By":[91],"analyzing":[92],"two-parameters":[94],"dependent":[95],"dynamics":[96],"system,":[99],"biparameter":[102],"zone":[103],"identified,":[105],"where":[106],"antimonotonicity":[107],"comes":[108],"into":[109],"existence.":[110],"complex":[112],"dynamical":[113],"behaviors":[114],"explored":[119],"using":[120],"phase":[121],"portraits,":[122],"bifurcation":[123],"diagrams,":[124],"Lyapunov":[125],"exponents,":[126],"isoperiodic":[127],"diagram,":[128],"basins":[130],"attraction.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}