{"id":"https://openalex.org/W7216289529","doi":"https://doi.org/10.48550/arxiv.2610.01868","title":"Multistability in the Duffing--Holmes oscillator: basins of antiperiodic, periodic, and chaotic attractors and their relative volumes","display_name":"Multistability in the Duffing--Holmes oscillator: basins of antiperiodic, periodic, and chaotic attractors and their relative volumes","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216289529","doi":"https://doi.org/10.48550/arxiv.2610.01868"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01868","pdf_url":"https://arxiv.org/pdf/2610.01868","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.01868","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155343134","display_name":"Arturo C. Marti","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Marti, Arturo C.","raw_affiliation_strings":[") Facultad de Ciencias , Universidad de la Rep\u00fablica , Igu\u00e1 4225 , Montevideo 11400 , Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":") Facultad de Ciencias , Universidad de la Rep\u00fablica , Igu\u00e1 4225 , Montevideo 11400 , Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5156163768","display_name":"Edson D. Leonel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Leonel, Edson D.","raw_affiliation_strings":[") Departamento de F\u00edsica , Universidade Estadual Paulista (UNESP) , Av. 24A 1515 , Rio Claro , S\u00e3o Paulo , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":") Departamento de F\u00edsica , Universidade Estadual Paulista (UNESP) , Av. 24A 1515 , Rio Claro , S\u00e3o Paulo , Brazil","institution_ids":["https://openalex.org/I879563668"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.6015999913215637,"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":0.6015999913215637,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.3490999937057495,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.024800000712275505,"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/duffing-holmes-oscillator","display_name":"Duffing-Holmes oscillator","score":0.9390000104904175},{"id":"https://openalex.org/keywords/multistability","display_name":"multistability","score":0.9800000190734863},{"id":"https://openalex.org/keywords/basins-of-attraction","display_name":"basins of attraction","score":0.8529999852180481},{"id":"https://openalex.org/keywords/periodic-attractors","display_name":"periodic attractors","score":0.8539999723434448},{"id":"https://openalex.org/keywords/strange-attractors","display_name":"chaotic attractors","score":0.9990000128746033},{"id":"https://openalex.org/keywords/coexisting-attractors","display_name":"coexisting attractors","score":0.7919999957084656},{"id":"https://openalex.org/keywords/stochastic-sampling","display_name":"stochastic sampling","score":0.48100000619888306},{"id":"https://openalex.org/keywords/bifurcation-diagrams","display_name":"bifurcation diagrams","score":0.7630000114440918}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7753000259399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6615999937057495},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.5996000170707703},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5645999908447266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5473999977111816},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.48570001125335693},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.446399986743927},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.34470000863075256},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C18932819","wikidata":"https://www.wikidata.org/wiki/Q2029236","display_name":"Stream function","level":4,"score":0.2750999927520752},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.27489998936653137},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.2721000015735626},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.27070000767707825},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01868","pdf_url":"https://arxiv.org/pdf/2610.01868","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.01868","doi":"https://doi.org/10.48550/arxiv.2610.01868","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01868","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.01868","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01868","pdf_url":"https://arxiv.org/pdf/2610.01868","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3789217090","display_name":null,"funder_award_id":"304398/2023-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6420761282","display_name":null,"funder_award_id":"304398/2023-3","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G9000846840","display_name":null,"funder_award_id":"2025/14544-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323603","display_name":"Universidad de la Rep\u00fablica Uruguay","ror":"https://ror.org/030bbe882"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216289529.pdf","grobid_xml":"https://content.openalex.org/works/W7216289529.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4415088259","https://openalex.org/W7167709052"],"related_works":["https://openalex.org/W4399445390","https://openalex.org/W7161782456","https://openalex.org/W7155108253","https://openalex.org/W2740752871","https://openalex.org/W4400915113","https://openalex.org/W4285020631","https://openalex.org/W2143885661","https://openalex.org/W6925342138","https://openalex.org/W7167709052","https://openalex.org/W4388943866"],"abstract_inverted_index":{"The":[0,167],"periodically":[1],"driven":[2],"Duffing--Holmes":[3],"oscillator":[4],"is":[5,71,165],"strongly":[6],"multistable:":[7],"for":[8],"the":[9,48,53,63,68,78,99,107,117,121,143,146,154,157,161,178,199,224,229,232,239,243,247,250,254,259,267,272],"same":[10,122],"forcing":[11,89,94,214],"amplitude":[12],"and":[13,17,91,249,270],"frequency,":[14],"periodic,":[15],"chaotic,":[16],"antiperiodic":[18,174,179,218,255],"attractors":[19,164,197],"coexist,":[20],"each":[21,111,150],"with":[22,43,228],"its":[23],"own":[24],"basin":[25,112,236,256],"of":[26,37,47,52,55,62,80,98,106,110,116,142,145,156,172,209,220,235,242,246,253],"attraction.":[27],"Antiperiodic":[28],"orbits":[29,32],"are":[30,130,238],"periodic":[31],"invariant":[33],"under":[34],"a":[35,39,44,50,59,114,216,263],"shift":[36],"half":[38],"driving":[40],"period":[41],"combined":[42],"sign":[45],"reversal":[46],"coordinates,":[49],"symmetry":[51],"equations":[54],"motion.":[56],"Guided":[57],"by":[58,132,140,187,262],"continuation":[60],"map":[61],"parameter":[64,123],"plane,":[65],"which":[66,126,177,191],"locates":[67],"regimes":[69],"but":[70],"blind":[72],"to":[73],"their":[74],"coexistence,":[75],"we":[76],"explore":[77],"space":[79,101,200],"initial":[81,151,184,268],"conditions":[82],"along":[83],"two":[84,192],"one-parameter":[85],"cuts,":[86],"at":[87,92,212],"fixed":[88,93],"frequency":[90],"amplitude.":[95],"Stochastic":[96],"sampling":[97],"full":[100],"yields":[102],"an":[103],"unbiased":[104],"estimate":[105],"relative":[108,168],"volume":[109,237],"as":[113,204,206],"function":[115],"control":[118],"parameter,":[119],"on":[120,125,136,266,271],"grids":[124],"single-trajectory":[127],"bifurcation":[128,230],"diagrams":[129],"computed":[131],"continuation.":[133],"Basin":[134],"maps":[135,141],"two-dimensional":[137],"sections,":[138],"complemented":[139],"order":[144,221],"attractor":[147],"reached":[148],"from":[149],"condition,":[152,185],"resolve":[153],"geometry":[155],"coexisting":[158],"basins":[159],"where":[160],"competition":[162],"between":[163],"strongest.":[166],"volumes":[169],"reveal":[170],"windows":[171],"global":[173],"dominance,":[175],"in":[176,190,201],"orbit":[180,219],"attracts":[181],"essentially":[182],"every":[183],"separated":[186],"narrow":[188],"intervals":[189],"or":[193],"three":[194],"qualitatively":[195],"different":[196],"share":[198],"comparable":[202],"proportions,":[203],"well":[205],"extended":[207],"ranges":[208],"persistent":[210],"coexistence;":[211],"large":[213],"amplitude,":[215],"single":[217],"one":[222],"captures":[223],"whole":[225],"space.":[226],"Compared":[227],"diagrams,":[231],"abrupt":[233],"changes":[234],"ensemble-level":[240],"counterpart":[241],"multistability-induced":[244],"discontinuities":[245],"sweeps,":[248],"gradual":[251],"shrinking":[252],"explains":[257],"why":[258],"branch":[260],"followed":[261],"sweep":[264],"depends":[265],"state":[269],"drive":[273],"phase.":[274]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}