{"id":"https://openalex.org/W2111848762","doi":"https://doi.org/10.1142/s0218127407019949","title":"ANALYTICAL DESCRIPTION OF RECURRENCE PLOTS OF DYNAMICAL SYSTEMS WITH NONTRIVIAL RECURRENCES","display_name":"ANALYTICAL DESCRIPTION OF RECURRENCE PLOTS OF DYNAMICAL SYSTEMS WITH NONTRIVIAL RECURRENCES","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W2111848762","doi":"https://doi.org/10.1142/s0218127407019949","mag":"2111848762"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407019949","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019949","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/A5007342254","display_name":"Yong Zou","orcid":"https://orcid.org/0000-0002-3241-3139"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Y. ZOU","raw_affiliation_strings":["Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009164900","display_name":"Marko Thiel","orcid":"https://orcid.org/0000-0002-7249-1203"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. THIEL","raw_affiliation_strings":["Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006279779","display_name":"M. Carmen Romano","orcid":"https://orcid.org/0000-0002-6261-2147"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. C. ROMANO","raw_affiliation_strings":["Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085207296","display_name":"J\u00fcrgen Kurths","orcid":"https://orcid.org/0000-0002-5926-4276"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. KURTHS","raw_affiliation_strings":["Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I176453806"],"apc_list":null,"apc_paid":null,"fwci":0.2594,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.59306532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"12","first_page":"4273","last_page":"4283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9957000017166138,"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":0.9957000017166138,"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":0.995199978351593,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9925000071525574,"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/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.9484074115753174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.669342041015625},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6322380304336548},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.619691789150238},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5744558572769165},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5664958953857422},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5165842771530151},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5030524134635925},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.46829739212989807},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4492201507091522},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.4318118393421173},{"id":"https://openalex.org/keywords/recurrence-quantification-analysis","display_name":"Recurrence quantification analysis","score":0.4162255525588989},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.4157818853855133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3837811350822449},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2421841025352478},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19110599160194397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15612900257110596},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08361297845840454},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06690424680709839}],"concepts":[{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.9484074115753174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.669342041015625},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6322380304336548},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.619691789150238},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5744558572769165},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5664958953857422},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5165842771530151},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5030524134635925},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.46829739212989807},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4492201507091522},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4318118393421173},{"id":"https://openalex.org/C43456602","wikidata":"https://www.wikidata.org/wiki/Q7303254","display_name":"Recurrence quantification analysis","level":3,"score":0.4162255525588989},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.4157818853855133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3837811350822449},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2421841025352478},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19110599160194397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15612900257110596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08361297845840454},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06690424680709839},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127407019949","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019949","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":[{"display_name":"Sustainable cities and communities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1492847513","https://openalex.org/W1972936364","https://openalex.org/W1978575993","https://openalex.org/W1985212113","https://openalex.org/W1989738639","https://openalex.org/W1997540084","https://openalex.org/W2002492329","https://openalex.org/W2040488623","https://openalex.org/W2044257293","https://openalex.org/W2050973980","https://openalex.org/W2081817659","https://openalex.org/W2090894422","https://openalex.org/W2099593264","https://openalex.org/W2100693443","https://openalex.org/W2102174702","https://openalex.org/W2108139264","https://openalex.org/W2113944951","https://openalex.org/W2131619958","https://openalex.org/W2156340241","https://openalex.org/W2489691424","https://openalex.org/W3045432724","https://openalex.org/W3133519615","https://openalex.org/W4212958445","https://openalex.org/W4242188978"],"related_works":["https://openalex.org/W1968995609","https://openalex.org/W3139111243","https://openalex.org/W2139086622","https://openalex.org/W2115021875","https://openalex.org/W1996986518","https://openalex.org/W1994358432","https://openalex.org/W2001811158","https://openalex.org/W2074751469","https://openalex.org/W3027681202","https://openalex.org/W2073549800"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,43,74],"study":[4],"recurrence":[5],"plots":[6],"(RPs)":[7],"for":[8,77,91],"the":[9,17,48,51,56,71],"simplest":[10],"example":[11],"of":[12,19,50,70,85,103],"nontrivial":[13,46],"recurrences,":[14,47],"namely":[15],"in":[16],"case":[18,24],"a":[20,32,67],"quasiperiodic":[21,81],"motion.":[22,82],"This":[23,64],"can":[25],"be":[26],"still":[27],"studied":[28],"analytically":[29,76],"and":[30,37,80],"constitutes":[31],"link":[33],"between":[34],"simple":[35],"periodic":[36,79],"more":[38],"complicated":[39],"chaotic":[40],"dynamics.":[41],"Since":[42],"deal":[44],"with":[45],"size":[49],"neighborhood":[52],"\u220a":[53,96],"to":[54,66,97],"which":[55,73],"trajectory":[57],"must":[58],"recur,":[59],"is":[60,89],"larger":[61],"than":[62],"zero.":[63],"leads":[65],"nonzero":[68],"width":[69],"lines,":[72],"determine":[75],"both":[78],"The":[83],"understanding":[84],"such":[86],"microscopic":[87],"structures":[88],"important":[90],"choosing":[92],"an":[93],"appropriate":[94],"threshold":[95],"analyze":[98],"experimental":[99],"data":[100],"by":[101],"means":[102],"RPs.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
