{"id":"https://openalex.org/W1870105587","doi":"https://doi.org/10.3390/e17085561","title":"A New Chaotic System with Positive Topological Entropy","display_name":"A New Chaotic System with Positive Topological Entropy","publication_year":2015,"publication_date":"2015-08-03","ids":{"openalex":"https://openalex.org/W1870105587","doi":"https://doi.org/10.3390/e17085561","mag":"1870105587"},"language":"en","primary_location":{"id":"doi:10.3390/e17085561","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17085561","pdf_url":"https://www.mdpi.com/1099-4300/17/8/5561/pdf?version=1438601452","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/1099-4300/17/8/5561/pdf?version=1438601452","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103084432","display_name":"Zhonglin Wang","orcid":"https://orcid.org/0000-0002-8860-5498"},"institutions":[{"id":"https://openalex.org/I151013683","display_name":"Binzhou University","ror":"https://ror.org/05frpfj73","country_code":"CN","type":"education","lineage":["https://openalex.org/I151013683"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhonglin Wang","raw_affiliation_strings":["Department of Physics and Electronics, Binzhou University, Binzhou 256600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Electronics, Binzhou University, Binzhou 256600, China","institution_ids":["https://openalex.org/I151013683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001349485","display_name":"Jian Ma","orcid":"https://orcid.org/0000-0002-9091-2040"},"institutions":[{"id":"https://openalex.org/I151013683","display_name":"Binzhou University","ror":"https://ror.org/05frpfj73","country_code":"CN","type":"education","lineage":["https://openalex.org/I151013683"]},{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Ma","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin 300071, China","Department of Physics and Electronics, Binzhou University, Binzhou 256600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Department of Physics and Electronics, Binzhou University, Binzhou 256600, China","institution_ids":["https://openalex.org/I151013683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073105796","display_name":"Zengqiang Chen","orcid":"https://orcid.org/0000-0002-1415-4073"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]},{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengqiang Chen","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin 300071, China","College of Science, Civil Aviation University of China, Tianjin 300300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin 300300, China","institution_ids":["https://openalex.org/I28813325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615838","display_name":"Qing Zhang","orcid":"https://orcid.org/0000-0003-3941-4764"},"institutions":[{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qing Zhang","raw_affiliation_strings":["College of Science, Civil Aviation University of China, Tianjin 300300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin 300300, China","institution_ids":["https://openalex.org/I28813325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103084432"],"corresponding_institution_ids":["https://openalex.org/I151013683"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1598,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77666462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"8","first_page":"5561","last_page":"5579"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9807000160217285,"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":0.9757999777793884,"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/topological-entropy","display_name":"Topological entropy","score":0.822819709777832},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7742281556129456},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.7433778047561646},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6679391860961914},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6578171253204346},{"id":"https://openalex.org/keywords/topological-entropy-in-physics","display_name":"Topological entropy in physics","score":0.5794368982315063},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5667099356651306},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5252463221549988},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.48340168595314026},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4721296429634094},{"id":"https://openalex.org/keywords/poincar\u00e9-map","display_name":"Poincar\u00e9 map","score":0.4230361878871918},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.415035218000412},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34835585951805115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2634061574935913},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19584447145462036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19217652082443237},{"id":"https://openalex.org/keywords/topological-quantum-number","display_name":"Topological quantum number","score":0.1559239625930786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14406415820121765},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07612985372543335}],"concepts":[{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.822819709777832},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7742281556129456},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7433778047561646},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6679391860961914},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6578171253204346},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.5794368982315063},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5667099356651306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5252463221549988},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48340168595314026},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4721296429634094},{"id":"https://openalex.org/C21955772","wikidata":"https://www.wikidata.org/wiki/Q339199","display_name":"Poincar\u00e9 map","level":4,"score":0.4230361878871918},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.415035218000412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34835585951805115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2634061574935913},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19584447145462036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19217652082443237},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.1559239625930786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14406415820121765},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07612985372543335},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e17085561","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17085561","pdf_url":"https://www.mdpi.com/1099-4300/17/8/5561/pdf?version=1438601452","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:c0f027e244a94ff59425e4edf174f1c7","is_oa":true,"landing_page_url":"https://doaj.org/article/c0f027e244a94ff59425e4edf174f1c7","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 17, Iss 8, Pp 5561-5579 (2015)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/17/8/5561/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e17085561","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/e17085561","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17085561","pdf_url":"https://www.mdpi.com/1099-4300/17/8/5561/pdf?version=1438601452","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1513878868","https://openalex.org/W1582770960","https://openalex.org/W1963864257","https://openalex.org/W1966278929","https://openalex.org/W1967008192","https://openalex.org/W1976581203","https://openalex.org/W1983053866","https://openalex.org/W1993301828","https://openalex.org/W1994859578","https://openalex.org/W2006839835","https://openalex.org/W2014509488","https://openalex.org/W2028438780","https://openalex.org/W2033530882","https://openalex.org/W2033818077","https://openalex.org/W2036870441","https://openalex.org/W2038494226","https://openalex.org/W2042736650","https://openalex.org/W2059368232","https://openalex.org/W2062124659","https://openalex.org/W2062427814","https://openalex.org/W2063055007","https://openalex.org/W2069436097","https://openalex.org/W2072769329","https://openalex.org/W2077887431","https://openalex.org/W2082172869","https://openalex.org/W2092680287","https://openalex.org/W2102892532","https://openalex.org/W2106154524","https://openalex.org/W2106201265","https://openalex.org/W2112602754","https://openalex.org/W2120458580","https://openalex.org/W2123893676","https://openalex.org/W2125566231","https://openalex.org/W2126098770","https://openalex.org/W2141394518","https://openalex.org/W2171987742","https://openalex.org/W2485547157","https://openalex.org/W4212928962","https://openalex.org/W4294967943","https://openalex.org/W6646113953","https://openalex.org/W6648874489","https://openalex.org/W6665952721","https://openalex.org/W6666049110","https://openalex.org/W6675813406"],"related_works":["https://openalex.org/W1987144560","https://openalex.org/W2366005415","https://openalex.org/W1821285933","https://openalex.org/W1966278929","https://openalex.org/W2097677799","https://openalex.org/W2809106743","https://openalex.org/W2080050855","https://openalex.org/W2782477056","https://openalex.org/W797434529","https://openalex.org/W2165253422"],"abstract_inverted_index":{"This":[0,12],"paper":[1],"introduces":[2],"a":[3,8,40,55],"new":[4,61,82],"simple":[5],"system":[6,13,52,62,83,102,114],"with":[7],"butterfly":[9],"chaotic":[10,33,37],"attractor.":[11],"has":[14,115],"rich":[15],"and":[16,45,73,93,111],"complex":[17],"dynamics.":[18],"With":[19],"some":[20],"typical":[21],"parameters,":[22,44],"its":[23],"Lyapunov":[24,66],"dimension":[25],"is":[26,53,103],"greater":[27],"than":[28],"other":[29],"known":[30],"three":[31],"dimensional":[32],"systems.":[34],"It":[35],"exhibits":[36],"behavior":[38],"over":[39],"large":[41],"range":[42],"of":[43,48,50,59,80,89],"the":[46,74,96,101,113],"divergence":[47],"flow":[49],"this":[51,60,81],"not":[54],"constant.":[56],"The":[57,77],"dynamics":[58],"are":[63,84],"analyzed":[64],"via":[65],"exponent":[67],"spectrum,":[68],"bifurcation":[69],"diagrams,":[70],"phase":[71],"portraits":[72],"Poincar\u00e9":[75,97],"map.":[76],"compound":[78],"structures":[79],"also":[85],"analyzed.":[86],"By":[87],"means":[88],"topological":[90,117],"horseshoe":[91],"theory":[92],"numerical":[94],"computation,":[95],"map":[98],"defined":[99],"for":[100],"proved":[104],"to":[105,108],"be":[106],"semi-conjugate":[107],"3-shift":[109],"map,":[110],"thus":[112],"positive":[116],"entropy.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}