{"id":"https://openalex.org/W2058752657","doi":"https://doi.org/10.3390/e16115618","title":"The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map","display_name":"The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map","publication_year":2014,"publication_date":"2014-10-27","ids":{"openalex":"https://openalex.org/W2058752657","doi":"https://doi.org/10.3390/e16115618","mag":"2058752657"},"language":"en","primary_location":{"id":"doi:10.3390/e16115618","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16115618","pdf_url":"https://www.mdpi.com/1099-4300/16/11/5618/pdf?version=1424785809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/11/5618/pdf?version=1424785809","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100326004","display_name":"Jiahui Liu","orcid":"https://orcid.org/0000-0002-5488-9138"},"institutions":[{"id":"https://openalex.org/I100188998","display_name":"Harbin University of Science and Technology","ror":"https://ror.org/04e6y1282","country_code":"CN","type":"education","lineage":["https://openalex.org/I100188998"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiahui Liu","raw_affiliation_strings":["College of Computer Science and Technology, Harbin Institute of Technology, P.O. Box 320,Harbin 150001, China","College of Computer Science and Technology, Harbin University of Science and Technology, P.O. Box 110, Harbin 150080, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Harbin Institute of Technology, P.O. Box 320,Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"College of Computer Science and Technology, Harbin University of Science and Technology, P.O. Box 110, Harbin 150080, China","institution_ids":["https://openalex.org/I100188998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100417312","display_name":"Hongli Zhang","orcid":"https://orcid.org/0000-0002-8167-7106"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongli Zhang","raw_affiliation_strings":["College of Computer Science and Technology, Harbin Institute of Technology, P.O. Box 320,Harbin 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Harbin Institute of Technology, P.O. Box 320,Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110364419","display_name":"Dahua Song","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093324","display_name":"Mudanjiang Medical University","ror":"https://ror.org/00mc5wj35","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210093324"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dahua Song","raw_affiliation_strings":["Center of Educational Technology and Information, Mudanjiang Medical University, Mudanjiang 157011, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Educational Technology and Information, Mudanjiang Medical University, Mudanjiang 157011, China","institution_ids":["https://openalex.org/I4210093324"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100326004"],"corresponding_institution_ids":["https://openalex.org/I100188998","https://openalex.org/I204983213"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.09957589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"16","issue":"11","first_page":"5618","last_page":"5632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9936000108718872,"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":0.9936000108718872,"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":0.9864000082015991,"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/T11786","display_name":"Geomagnetism and Paleomagnetism Studies","score":0.9790999889373779,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logistic-map","display_name":"Logistic map","score":0.8232104778289795},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.7509118318557739},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.7131274938583374},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.6955276727676392},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6420891284942627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5393561720848083},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5222907066345215},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.44870132207870483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36089301109313965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35796940326690674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19768619537353516},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17897507548332214},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07156398892402649}],"concepts":[{"id":"https://openalex.org/C205330730","wikidata":"https://www.wikidata.org/wiki/Q587182","display_name":"Logistic map","level":3,"score":0.8232104778289795},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.7509118318557739},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.7131274938583374},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.6955276727676392},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6420891284942627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5393561720848083},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5222907066345215},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.44870132207870483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36089301109313965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35796940326690674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19768619537353516},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17897507548332214},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07156398892402649},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e16115618","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16115618","pdf_url":"https://www.mdpi.com/1099-4300/16/11/5618/pdf?version=1424785809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ba2f9af4226d4b4eb608e922a21c884b","is_oa":true,"landing_page_url":"https://doaj.org/article/ba2f9af4226d4b4eb608e922a21c884b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 16, Iss 11, Pp 5618-5632 (2014)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/11/5618/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e16115618","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e16115618","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16115618","pdf_url":"https://www.mdpi.com/1099-4300/16/11/5618/pdf?version=1424785809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1106358333","display_name":null,"funder_award_id":"2011CB302605","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4243412236","display_name":null,"funder_award_id":"863 Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G576806752","display_name":null,"funder_award_id":"2011CB302605","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322217","display_name":"Department of Education, Heilongjiang Province","ror":"https://ror.org/04rn1rm44"},{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null},{"id":"https://openalex.org/F4320335773","display_name":"National High-tech Research and Development Program","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2058752657.pdf","grobid_xml":"https://content.openalex.org/works/W2058752657.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1976426545","https://openalex.org/W1984529470","https://openalex.org/W1991453283","https://openalex.org/W1992120986","https://openalex.org/W1997137389","https://openalex.org/W2015304581","https://openalex.org/W2020480302","https://openalex.org/W2020870384","https://openalex.org/W2037254051","https://openalex.org/W2039051675","https://openalex.org/W2044244729","https://openalex.org/W2050128379","https://openalex.org/W2066395581","https://openalex.org/W2072963358","https://openalex.org/W2087045023","https://openalex.org/W2091285247","https://openalex.org/W2092737172"],"related_works":["https://openalex.org/W2006887475","https://openalex.org/W2388148802","https://openalex.org/W2377672665","https://openalex.org/W2055371868","https://openalex.org/W2903140093","https://openalex.org/W1567811277","https://openalex.org/W2994758972","https://openalex.org/W2018914863","https://openalex.org/W1987248656","https://openalex.org/W2538527336"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"an":[5],"iterative":[6],"method":[7],"with":[8],"lower":[9,74],"positions":[10,75],"of":[11,26,33,41,59,76,88],"true":[12,78],"numerical":[13,79],"solutions":[14,80],"located":[15],"in":[16,20,81],"the":[17,24,27,34,42,46,51,60,66,73,77,82,86],"real":[18,83],"orbit":[19],"order":[21],"to":[22],"investigate":[23],"property":[25,87],"logistic":[28,35,61],"map.":[29],"The":[30,55],"basic":[31],"structure":[32],"map":[36,62],"is":[37],"presented,":[38],"which":[39],"consists":[40],"root":[43],"gene":[44,48,53,68],"position,":[45],"common":[47],"position":[49],"and":[50,57],"individual":[52,67],"position.":[54,69],"ergodicity":[56],"randomness":[58],"are":[63],"dependent":[64],"on":[65],"We":[70],"find":[71],"that":[72],"orbits":[84],"have":[85],"a":[89],"half-life.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
