{"id":"https://openalex.org/W2283802939","doi":"https://doi.org/10.1142/s0218127416500127","title":"Invariant Approach to Existence Problem of Chaos in 3D Autonomous Quadratic Dynamical Systems","display_name":"Invariant Approach to Existence Problem of Chaos in 3D Autonomous Quadratic Dynamical Systems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2283802939","doi":"https://doi.org/10.1142/s0218127416500127","mag":"2283802939"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500127","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500127","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/A5068160516","display_name":"Vasiliy Ye. Belozyorov","orcid":"https://orcid.org/0000-0002-9652-7303"},"institutions":[{"id":"https://openalex.org/I883679329","display_name":"Oles Honchar Dnipro National University","ror":"https://ror.org/00qk1f078","country_code":"UA","type":"education","lineage":["https://openalex.org/I883679329"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Vasiliy Ye. Belozyorov","raw_affiliation_strings":["Department of Applied Mathematics, Dnepropetrovsk National University, Gagarin\u2019s Avenue, 72, 49050 Dnepropetrovsk, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Dnepropetrovsk National University, Gagarin\u2019s Avenue, 72, 49050 Dnepropetrovsk, Ukraine","institution_ids":["https://openalex.org/I883679329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068160516"],"corresponding_institution_ids":["https://openalex.org/I883679329"],"apc_list":null,"apc_paid":null,"fwci":3.1958,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90437172,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"26","issue":"01","first_page":"1650012","last_page":"1650012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9955000281333923,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9955000281333923,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9882000088691711,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.705800473690033},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7014285326004028},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.673671305179596},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6368691325187683},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.49468013644218445},{"id":"https://openalex.org/keywords/solving-quadratic-equations-with-continued-fractions","display_name":"Solving quadratic equations with continued fractions","score":0.4582679569721222},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.45525065064430237},{"id":"https://openalex.org/keywords/autonomous-system","display_name":"Autonomous system (mathematics)","score":0.45090168714523315},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.4431108832359314},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4371778666973114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4281593859195709},{"id":"https://openalex.org/keywords/quadratic-differential","display_name":"Quadratic differential","score":0.4279389977455139},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34665554761886597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3322879672050476},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.31354743242263794},{"id":"https://openalex.org/keywords/binary-quadratic-form","display_name":"Binary quadratic form","score":0.1893221139907837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15785002708435059},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10938587784767151},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07532668113708496}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.705800473690033},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7014285326004028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.673671305179596},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6368691325187683},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.49468013644218445},{"id":"https://openalex.org/C126949999","wikidata":"https://www.wikidata.org/wiki/Q1212495","display_name":"Solving quadratic equations with continued fractions","level":5,"score":0.4582679569721222},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.45525065064430237},{"id":"https://openalex.org/C9628104","wikidata":"https://www.wikidata.org/wiki/Q788009","display_name":"Autonomous system (mathematics)","level":2,"score":0.45090168714523315},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.4431108832359314},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4371778666973114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4281593859195709},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.4279389977455139},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34665554761886597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3322879672050476},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.31354743242263794},{"id":"https://openalex.org/C80695182","wikidata":"https://www.wikidata.org/wiki/Q864134","display_name":"Binary quadratic form","level":4,"score":0.1893221139907837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15785002708435059},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10938587784767151},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07532668113708496},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500127","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500127","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1941862748","https://openalex.org/W1964959594","https://openalex.org/W2012138759","https://openalex.org/W2021766441","https://openalex.org/W2023222439","https://openalex.org/W2029150179","https://openalex.org/W2033042940","https://openalex.org/W2042868976","https://openalex.org/W2064417168","https://openalex.org/W2080225290","https://openalex.org/W2082745089","https://openalex.org/W2092360752","https://openalex.org/W2113246250","https://openalex.org/W2116793592","https://openalex.org/W2129845849"],"related_works":["https://openalex.org/W4386731488","https://openalex.org/W2625742927","https://openalex.org/W4299819625","https://openalex.org/W2033982406","https://openalex.org/W1996159914","https://openalex.org/W269925151","https://openalex.org/W2931186781","https://openalex.org/W1997272315","https://openalex.org/W1966709319","https://openalex.org/W2283802939"],"abstract_inverted_index":{"New":[0],"existence":[1],"conditions":[2,18],"of":[3,9,26,28],"chaos":[4],"for":[5,31],"a":[6],"wide":[7],"class":[8],"3D":[10],"autonomous":[11],"quadratic":[12,34],"dynamical":[13],"systems":[14],"are":[15,19],"suggested.":[16],"These":[17],"based":[20],"on":[21],"the":[22],"construction":[23],"and":[24],"study":[25],"properties":[27],"algebraic":[29],"invariants":[30],"some":[32],"2D":[33],"system":[35],"differential":[36],"equations.":[37]},"counts_by_year":[{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
