{"id":"https://openalex.org/W3209153251","doi":"https://doi.org/10.1142/s0218127421501947","title":"Complexity in a Hybrid van der Pol System","display_name":"Complexity in a Hybrid van der Pol System","publication_year":2021,"publication_date":"2021-10-01","ids":{"openalex":"https://openalex.org/W3209153251","doi":"https://doi.org/10.1142/s0218127421501947","mag":"3209153251"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421501947","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421501947","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/A5046234526","display_name":"Vincent Naudot","orcid":"https://orcid.org/0000-0002-9483-6874"},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vincent Naudot","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA"],"raw_orcid":"https://orcid.org/0000-0002-9483-6874","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030270091","display_name":"Shane Kepley","orcid":"https://orcid.org/0000-0001-6447-9418"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shane Kepley","raw_affiliation_strings":["Department of Mathematics, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004040775","display_name":"William D. Kalies","orcid":"https://orcid.org/0000-0002-8228-3598"},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William D. Kalies","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA","institution_ids":["https://openalex.org/I63772739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1282,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46551639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"13","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980000257492065,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980000257492065,"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/T10244","display_name":"Chaos control and synchronization","score":0.9916999936103821,"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":0.9589999914169312,"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":0.8796294927597046},{"id":"https://openalex.org/keywords/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.823975682258606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6712355017662048},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6436249017715454},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6346558332443237},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6261851191520691},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5596343874931335},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5233582258224487},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5127416849136353},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.4637942910194397},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.45213431119918823},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4489148259162903},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4281073212623596},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.418704092502594},{"id":"https://openalex.org/keywords/slow-manifold","display_name":"Slow manifold","score":0.4117034673690796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37344396114349365},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.24211865663528442},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17944779992103577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16944962739944458},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1482154130935669},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11653795838356018}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8796294927597046},{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.823975682258606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6712355017662048},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6436249017715454},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6346558332443237},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6261851191520691},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5596343874931335},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5233582258224487},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5127416849136353},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.4637942910194397},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.45213431119918823},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4489148259162903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4281073212623596},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.418704092502594},{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.4117034673690796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37344396114349365},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.24211865663528442},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17944779992103577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16944962739944458},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1482154130935669},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11653795838356018},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421501947","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421501947","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W178772886","https://openalex.org/W306903215","https://openalex.org/W1981833819","https://openalex.org/W1984029601","https://openalex.org/W1989018928","https://openalex.org/W1994266397","https://openalex.org/W1995249182","https://openalex.org/W2018008514","https://openalex.org/W2019398782","https://openalex.org/W2031022267","https://openalex.org/W2036319645","https://openalex.org/W2041160720","https://openalex.org/W2042795808","https://openalex.org/W2076033814","https://openalex.org/W2077011938","https://openalex.org/W2083184107","https://openalex.org/W2083968745","https://openalex.org/W2095039299","https://openalex.org/W2112602754","https://openalex.org/W2119972831","https://openalex.org/W2121020818","https://openalex.org/W2125566231","https://openalex.org/W2143945573","https://openalex.org/W2151960255","https://openalex.org/W2171689276","https://openalex.org/W2246188494","https://openalex.org/W2294040392","https://openalex.org/W2317893523","https://openalex.org/W2335681000","https://openalex.org/W2339075642","https://openalex.org/W2470889287","https://openalex.org/W2597083622","https://openalex.org/W2727020437","https://openalex.org/W2757389357","https://openalex.org/W2805288495","https://openalex.org/W2963906850","https://openalex.org/W2972531149","https://openalex.org/W3182252275","https://openalex.org/W4239981491","https://openalex.org/W4252911570","https://openalex.org/W4254246953"],"related_works":["https://openalex.org/W3165421822","https://openalex.org/W2043393553","https://openalex.org/W2055410928","https://openalex.org/W3004031260","https://openalex.org/W2129195111","https://openalex.org/W2003467148","https://openalex.org/W2002931758","https://openalex.org/W1010944416","https://openalex.org/W106290298","https://openalex.org/W1972846926"],"abstract_inverted_index":{"In":[0],"this":[1,31],"work,":[2],"we":[3],"study,":[4],"from":[5],"a":[6,14,36,64,68,77,92,105,143],"numerical":[7,69,137],"point":[8],"of":[9,13,21,30,48,76,88,94,104,124,142,150,154],"view,":[10],"the":[11,22,39,43,49,54,60,89,95,98,125,140,148,151,155],"dynamics":[12,29,96],"specific":[15,122],"hybrid":[16],"map":[17,47],"which":[18,81],"is":[19,33,42,63,100],"that":[20],"kicked":[23],"van":[24,55],"der":[25,56],"Pol":[26,57],"system.":[27],"The":[28],"system":[32],"generated":[34],"by":[35,110,119],"two-stage":[37],"procedure:":[38],"first":[40],"stage":[41,62],"time-[Formula:":[44],"see":[45],"text]":[46],"vector":[50],"field":[51],"associated":[52],"with":[53],"equation,":[58],"and":[59,109,129],"second":[61],"translation.":[65],"We":[66,115],"propose":[67],"method":[70],"for":[71],"computing":[72],"local":[73],"(un)stable":[74],"manifolds":[75,131],"given":[78],"fixed":[79,156],"point,":[80],"leads":[82],"to":[83],"high":[84],"order":[85],"polynomial":[86],"parameterization":[87],"embedding.":[90],"Such":[91],"representation":[93],"on":[97],"manifold":[99,153],"obtained":[101],"in":[102,147],"terms":[103],"simple":[106],"conjugacy":[107],"relation":[108],"constructing":[111],"two":[112],"contracting":[113],"operators.":[114],"illustrate":[116],"our":[117,136],"techniques":[118],"plotting":[120],"(for":[121],"values":[123],"parameters)":[126],"both":[127],"stable":[128],"unstable":[130,152],"displaying":[132],"homoclinic":[133],"intersection.":[134],"Furthermore,":[135],"study":[138],"reveals":[139],"presence":[141],"strange":[144],"attractor":[145],"included":[146],"closure":[149],"point.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}