{"id":"https://openalex.org/W2563581845","doi":"https://doi.org/10.1142/s0218127416502199","title":"Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems","display_name":"Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems","publication_year":2016,"publication_date":"2016-12-15","ids":{"openalex":"https://openalex.org/W2563581845","doi":"https://doi.org/10.1142/s0218127416502199","mag":"2563581845"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416502199","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502199","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/A5022712564","display_name":"Jianbin He","orcid":"https://orcid.org/0000-0003-4098-7869"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianbin He","raw_affiliation_strings":["College of Automation, Guangdong University of Technology, Guangzhou 510006, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Guangdong University of Technology, Guangzhou 510006, P. R. China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013127565","display_name":"Simin Yu","orcid":"https://orcid.org/0000-0002-1192-6955"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Simin Yu","raw_affiliation_strings":["College of Automation, Guangdong University of Technology, Guangzhou 510006, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automation, Guangdong University of Technology, Guangzhou 510006, P. R. China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073988347","display_name":"Jianping Cai","orcid":"https://orcid.org/0000-0001-9882-3782"},"institutions":[{"id":"https://openalex.org/I9356336","display_name":"Minnan Normal University","ror":"https://ror.org/02vj1vm13","country_code":"CN","type":"education","lineage":["https://openalex.org/I9356336"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping Cai","raw_affiliation_strings":["College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, P. R. China","institution_ids":["https://openalex.org/I9356336"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5727,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.69633125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"13","first_page":"1650219","last_page":"1650219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9939000010490417,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9463000297546387,"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":0.9537163972854614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.667870283126831},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6006940007209778},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5985684394836426},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5894996523857117},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5492059588432312},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.4228220582008362},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4118194282054901},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3261854946613312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24861150979995728}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.9537163972854614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.667870283126831},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6006940007209778},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5985684394836426},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5894996523857117},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5492059588432312},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.4228220582008362},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4118194282054901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3261854946613312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24861150979995728},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416502199","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502199","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":26,"referenced_works":["https://openalex.org/W1496745782","https://openalex.org/W1559523057","https://openalex.org/W1972926236","https://openalex.org/W1984317615","https://openalex.org/W1998538686","https://openalex.org/W1998727969","https://openalex.org/W1999517614","https://openalex.org/W2012315426","https://openalex.org/W2021684685","https://openalex.org/W2031057566","https://openalex.org/W2042619282","https://openalex.org/W2046732414","https://openalex.org/W2055660413","https://openalex.org/W2059340344","https://openalex.org/W2062908485","https://openalex.org/W2072998188","https://openalex.org/W2085125527","https://openalex.org/W2092961463","https://openalex.org/W2139153229","https://openalex.org/W2152254020","https://openalex.org/W2249740901","https://openalex.org/W3098807575","https://openalex.org/W3105798161","https://openalex.org/W4230976146","https://openalex.org/W4239883234","https://openalex.org/W4248796009"],"related_works":["https://openalex.org/W2320400738","https://openalex.org/W2013611044","https://openalex.org/W2367467130","https://openalex.org/W2365327494","https://openalex.org/W2952844933","https://openalex.org/W1802951461","https://openalex.org/W1984625617","https://openalex.org/W2077215839","https://openalex.org/W2511980821","https://openalex.org/W2388583392"],"abstract_inverted_index":{"Lyapunov":[0,14,33,52,133,141],"exponent":[1,15,53],"is":[2,24],"an":[3,38,107],"important":[4],"index":[5],"for":[6],"describing":[7],"chaotic":[8,25],"systems":[9],"behavior,":[10],"and":[11,62,75,189,210],"the":[12,32,47,58,63,70,78,101,116,128,139,151,158,164,171,198,208,213],"largest":[13,140],"can":[16,54,88],"be":[17,55,81,89,97],"used":[18],"to":[19,44,69,138,145,196,206],"determine":[20],"whether":[21],"a":[22],"system":[23],"or":[26,85,112,121],"not.":[27],"For":[28],"discrete-time":[29,177],"dynamical":[30],"systems,":[31,178],"exponents":[34,134],"are":[35,160,166,204],"calculated":[36],"by":[37],"eigenvalue":[39,45],"method.":[40],"In":[41],"theory,":[42],"according":[43],"method,":[46],"more":[48],"accurate":[49],"calculations":[50],"of":[51,60,73,110,119,130,153,173,212],"obtained":[56],"with":[57,127],"increment":[59,129],"iterations,":[61,131],"limits":[64],"also":[65,167],"exist.":[66],"However,":[67],"due":[68],"finite":[71],"precision":[72],"computer":[74],"other":[76],"reasons,":[77],"results":[79,165],"will":[80,104,135],"numeric":[82],"overflow,":[83],"unrecognized,":[84],"inaccurate,":[86],"which":[87,143],"stated":[90],"as":[91,106,195],"follows:":[92],"(1)":[93],"The":[94],"iterations":[95,159],"cannot":[96],"too":[98,161],"large,":[99],"otherwise,":[100],"simulation":[102],"result":[103],"appear":[105],"error":[108,117],"message":[109,118],"NaN":[111,120],"Inf;":[113],"(2)":[114],"If":[115],"Inf":[122],"does":[123],"not":[124],"appear,":[125],"then":[126,163],"all":[132],"get":[136],"close":[137],"exponent,":[142],"leads":[144],"inaccurate":[146],"calculation":[147,175],"results;":[148],"(3)":[149],"From":[150],"viewpoint":[152],"numerical":[154],"calculation,":[155],"obviously,":[156],"if":[157],"small,":[162],"inaccurate.":[168],"Based":[169],"on":[170],"analysis":[172],"Lyapunov-exponent":[174],"in":[176],"this":[179],"paper":[180],"investigates":[181],"two":[182],"improved":[183,214],"algorithms":[184],"via":[185],"QR":[186],"orthogonal":[187,191],"decomposition":[188,192],"SVD":[190],"approaches":[193],"so":[194],"solve":[197],"above-mentioned":[199],"problems.":[200],"Finally,":[201],"some":[202],"examples":[203],"given":[205],"illustrate":[207],"feasibility":[209],"effectiveness":[211],"algorithms.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
