{"id":"https://openalex.org/W4402525283","doi":"https://doi.org/10.3390/axioms13090625","title":"Dynamics of a New Four-Thirds-Degree Sub-Quadratic Lorenz-like System","display_name":"Dynamics of a New Four-Thirds-Degree Sub-Quadratic Lorenz-like System","publication_year":2024,"publication_date":"2024-09-12","ids":{"openalex":"https://openalex.org/W4402525283","doi":"https://doi.org/10.3390/axioms13090625"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13090625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090625","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13090625","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020915389","display_name":"Guiyao Ke","orcid":"https://orcid.org/0000-0002-6467-9759"},"institutions":[{"id":"https://openalex.org/I4210100550","display_name":"Zhejiang DongFang Vocational and Technical College","ror":"https://ror.org/00yejqr65","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210100550"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiyao Ke","raw_affiliation_strings":["School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China"],"raw_orcid":"https://orcid.org/0000-0002-6467-9759","affiliations":[{"raw_affiliation_string":"School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China","institution_ids":["https://openalex.org/I4210100550"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035269751","display_name":"Jun Pan","orcid":"https://orcid.org/0000-0002-2994-5070"},"institutions":[{"id":"https://openalex.org/I168879160","display_name":"Zhejiang University of Science and Technology","ror":"https://ror.org/05mx0wr29","country_code":"CN","type":"education","lineage":["https://openalex.org/I168879160"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Pan","raw_affiliation_strings":["Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China"],"raw_orcid":"https://orcid.org/0000-0002-2994-5070","affiliations":[{"raw_affiliation_string":"Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China","institution_ids":["https://openalex.org/I168879160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007814699","display_name":"Feiyu Hu","orcid":"https://orcid.org/0000-0002-1800-9826"},"institutions":[{"id":"https://openalex.org/I157921009","display_name":"Ritsumeikan Asia Pacific University","ror":"https://ror.org/03ynn1n59","country_code":"JP","type":"education","lineage":["https://openalex.org/I157921009","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Feiyu Hu","raw_affiliation_strings":["College of Sustainability and Tourism, Ritsumeikan Asia Pacific University, Beppu 874-8577, Oita, Japan"],"raw_orcid":"https://orcid.org/0000-0002-1800-9826","affiliations":[{"raw_affiliation_string":"College of Sustainability and Tourism, Ritsumeikan Asia Pacific University, Beppu 874-8577, Oita, Japan","institution_ids":["https://openalex.org/I157921009"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100419354","display_name":"Haijun Wang","orcid":"https://orcid.org/0000-0002-0648-4910"},"institutions":[{"id":"https://openalex.org/I82760581","display_name":"Taizhou University","ror":"https://ror.org/04fzhyx73","country_code":"CN","type":"education","lineage":["https://openalex.org/I82760581"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haijun Wang","raw_affiliation_strings":["School of Electronic and Information Engineering, Taizhou University, Taizhou 318000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Taizhou University, Taizhou 318000, China","institution_ids":["https://openalex.org/I82760581"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035269751"],"corresponding_institution_ids":["https://openalex.org/I168879160"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.9928,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74688065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"13","issue":"9","first_page":"625","last_page":"625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9995999932289124,"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":0.9995999932289124,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.732063353061676},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.6791934370994568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6738094687461853},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6222347021102905},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.5711075067520142},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.5626975297927856},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5413416028022766},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4414653778076172},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.44059503078460693},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43798547983169556},{"id":"https://openalex.org/keywords/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.4246619939804077},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.41493335366249084},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3954654335975647},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3799675405025482},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.3715059757232666},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20015689730644226},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.18296265602111816},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09584447741508484},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08710569143295288}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.732063353061676},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.6791934370994568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6738094687461853},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6222347021102905},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5711075067520142},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.5626975297927856},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5413416028022766},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4414653778076172},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.44059503078460693},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43798547983169556},{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.4246619939804077},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41493335366249084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3954654335975647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3799675405025482},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.3715059757232666},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20015689730644226},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.18296265602111816},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09584447741508484},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08710569143295288},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13090625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090625","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:afbb264caafe4ef2bf7b4574affb51e5","is_oa":false,"landing_page_url":"https://doaj.org/article/afbb264caafe4ef2bf7b4574affb51e5","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 9, p 625 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13090625","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090625","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1582770960","https://openalex.org/W1596321532","https://openalex.org/W1965257932","https://openalex.org/W1992474007","https://openalex.org/W2015096633","https://openalex.org/W2019398782","https://openalex.org/W2024862895","https://openalex.org/W2025846951","https://openalex.org/W2029750936","https://openalex.org/W2040704758","https://openalex.org/W2044413922","https://openalex.org/W2049576731","https://openalex.org/W2052311828","https://openalex.org/W2058099048","https://openalex.org/W2060438851","https://openalex.org/W2076977710","https://openalex.org/W2091402091","https://openalex.org/W2141394518","https://openalex.org/W2151523878","https://openalex.org/W2154371151","https://openalex.org/W2346673812","https://openalex.org/W2602396255","https://openalex.org/W2731907499","https://openalex.org/W2926309618","https://openalex.org/W2999385695","https://openalex.org/W3048600509","https://openalex.org/W4206357236","https://openalex.org/W4387495070","https://openalex.org/W4390155012","https://openalex.org/W4391036820","https://openalex.org/W4396938641","https://openalex.org/W4398216222","https://openalex.org/W4399741132","https://openalex.org/W6655116729","https://openalex.org/W6673435985","https://openalex.org/W6772902062","https://openalex.org/W6880910875"],"related_works":["https://openalex.org/W2095803285","https://openalex.org/W2102865807","https://openalex.org/W2923981205","https://openalex.org/W2048268923","https://openalex.org/W4366813520","https://openalex.org/W2559450076","https://openalex.org/W2025846951","https://openalex.org/W2902201712","https://openalex.org/W2267377916","https://openalex.org/W2599487117"],"abstract_inverted_index":{"Aiming":[0],"to":[1,144],"explore":[2],"the":[3,7,34,41,44,61,64,86,90,107,132,135,139,149,161],"subtle":[4],"connection":[5],"between":[6],"number":[8,150],"of":[9,37,43,63,85,89,134,138,154,163],"nonlinear":[10,45],"terms":[11,46],"in":[12,47],"Lorenz-like":[13,26,50,98],"systems":[14],"and":[15,32,81,102,124,151,156],"hidden":[16,68],"attractors,":[17,69,99],"this":[18],"paper":[19],"introduces":[20],"a":[21,48],"new":[22],"simple":[23],"sub-quadratic":[24],"four-thirds-degree":[25],"system,":[27],"where":[28,52],"x\u02d9=a(y\u2212x),":[29,53],"y\u02d9=cx\u2212x3z,":[30],"z\u02d9=\u2212bz+x3y,":[31],"uncovers":[33],"following":[35],"property":[36],"these":[38],"systems:":[39],"decreasing":[40],"powers":[42],"quadratic":[49],"system":[51,92],"y\u02d9=cx\u2212xz,":[54],"z\u02d9=\u2212bz+xy,":[55],"may":[56,130,158],"narrow,":[57],"or":[58],"even":[59],"eliminate":[60],"range":[62],"parameter":[65],"c":[66],"for":[67,73],"but":[70],"enlarge":[71],"it":[72],"self-excited":[74,97],"attractors.":[75],"By":[76],"combining":[77],"numerical":[78],"simulation,":[79],"stability":[80],"bifurcation":[82,101,105,115],"theory,":[83],"most":[84],"important":[87],"dynamics":[88],"Lorenz":[91],"family":[93],"are":[94],"revealed,":[95],"including":[96],"Hopf":[100],"generic":[103],"pitchfork":[104,114],"at":[106,116],"origin,":[108],"singularly":[109],"degenerate":[110,113],"heteroclinic":[111,122],"cycles,":[112],"non-isolated":[117],"equilibria,":[118],"invariant":[119],"algebraic":[120],"surface,":[121],"orbits":[123],"so":[125],"on.":[126],"The":[127],"obtained":[128],"results":[129],"verify":[131],"generalization":[133],"second":[136],"part":[137],"celebrated":[140],"Hilbert\u2019s":[141],"sixteenth":[142],"problem":[143],"some":[145],"degree,":[146],"showing":[147],"that":[148],"mutual":[152],"disposition":[153],"attractors":[155],"repellers":[157],"depend":[159],"on":[160],"degree":[162],"chaotic":[164],"multidimensional":[165],"dynamical":[166],"systems.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}