{"id":"https://openalex.org/W1998397211","doi":"https://doi.org/10.1142/s021812740701780x","title":"A COMPUTER-ASSISTED STUDY OF GLOBAL DYNAMIC TRANSITIONS FOR A NONINVERTIBLE SYSTEM","display_name":"A COMPUTER-ASSISTED STUDY OF GLOBAL DYNAMIC TRANSITIONS FOR A NONINVERTIBLE SYSTEM","publication_year":2007,"publication_date":"2007-04-01","ids":{"openalex":"https://openalex.org/W1998397211","doi":"https://doi.org/10.1142/s021812740701780x","mag":"1998397211"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740701780x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740701780x","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/A5112459598","display_name":"Raymond A. Adomaitis","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"RAYMOND A. ADOMAITIS","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036566464","display_name":"Ioannis G. Kevrekidis","orcid":"https://orcid.org/0000-0003-2220-3522"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"IOANNIS G. KEVREKIDIS","raw_affiliation_strings":["Department of Chemical Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004732229","display_name":"Rafael de la Llave","orcid":"https://orcid.org/0000-0002-0286-6233"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"RAFAEL DE LA LLAVE","raw_affiliation_strings":["Department of Mathematics, 1 University Station C1200, University of Texas, Austin, TX 78712, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, 1 University Station C1200, University of Texas, Austin, TX 78712, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0106,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78658216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"17","issue":"04","first_page":"1305","last_page":"1321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9980999827384949,"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/T10244","display_name":"Chaos control and synchronization","score":0.9955999851226807,"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":0.9879999756813049,"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/phase-space","display_name":"Phase space","score":0.6327871084213257},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6262177228927612},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6125905513763428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5839669704437256},{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.5573611259460449},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5299336314201355},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.49180272221565247},{"id":"https://openalex.org/keywords/breakup","display_name":"Breakup","score":0.4839951992034912},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44225820899009705},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4158356189727783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3592144250869751},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3293529748916626},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17943689227104187},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1600187122821808}],"concepts":[{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6327871084213257},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6262177228927612},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6125905513763428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5839669704437256},{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.5573611259460449},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5299336314201355},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.49180272221565247},{"id":"https://openalex.org/C2777871205","wikidata":"https://www.wikidata.org/wiki/Q100926628","display_name":"Breakup","level":2,"score":0.4839951992034912},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44225820899009705},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4158356189727783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3592144250869751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3293529748916626},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17943689227104187},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1600187122821808},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812740701780x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740701780x","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":[{"id":"https://metadata.un.org/sdg/11","score":0.5099999904632568,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W331846077","https://openalex.org/W1564678287","https://openalex.org/W1963792091","https://openalex.org/W1974302683","https://openalex.org/W1975030700","https://openalex.org/W1975468503","https://openalex.org/W1987251863","https://openalex.org/W1988796640","https://openalex.org/W1995650502","https://openalex.org/W1996473620","https://openalex.org/W1996578686","https://openalex.org/W2046557303","https://openalex.org/W2053612038","https://openalex.org/W2055333402","https://openalex.org/W2055841241","https://openalex.org/W2074147617","https://openalex.org/W2081510730","https://openalex.org/W2083968850"],"related_works":["https://openalex.org/W2806947080","https://openalex.org/W1999870068","https://openalex.org/W2897298191","https://openalex.org/W2084508465","https://openalex.org/W3102978429","https://openalex.org/W2079284867","https://openalex.org/W2049111552","https://openalex.org/W3180125187","https://openalex.org/W1979553448","https://openalex.org/W1999621897"],"abstract_inverted_index":{"We":[0],"present":[1,64],"a":[2,13,54,69],"computer-assisted":[3],"analysis":[4],"of":[5,12,30,35,42,52,108,111],"the":[6,21,33,73,106,109],"phase":[7,76,91],"space":[8,92],"features":[9,93],"and":[10,32,47,89,103],"bifurcations":[11,102],"noninvertible,":[14],"discrete-time":[15],"system.":[16],"Our":[17],"focus":[18],"is":[19,94],"on":[20],"role":[22],"played":[23],"by":[24],"noninvertibility":[25],"in":[26,58,99,105],"generating":[27],"disconnected":[28],"basins":[29],"attraction":[31,43],"breakup":[34],"invariant":[36],"circle":[37],"solutions.":[38],"Transitions":[39],"between":[40,86],"basin":[41,110],"structures":[44],"are":[45],"identified":[46],"organized":[48],"according":[49],"to":[50,72,96],"\"levels":[51],"complexity,\"":[53],"term":[55],"we":[56,63],"define":[57],"this":[59,87],"paper.":[60],"In":[61],"particular,":[62],"an":[65],"algorithm":[66],"that":[67],"provides":[68],"computational":[70],"approximation":[71],"boundary":[74,88],"(in":[75],"space)":[77],"separating":[78],"points":[79],"with":[80],"different":[81],"preimage":[82],"behavior.":[83],"The":[84],"interplay":[85],"other":[90],"shown":[95],"be":[97],"crucial":[98],"understanding":[100],"global":[101],"transitions":[104],"structure":[107],"attraction.":[112]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}