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The algebraic criterion presented here is proved using some ideas from the Darboux theory of integrability, such as the existence of invariant algebraic surfaces and Darboux invariants, and is quite general, hence it can be used to study the nonchaotic behavior of other types of differential systems defined in [Formula: see text], including polynomial differential systems of any degree having (or not having) a symmetric Jacobian matrix. <\/jats:p>","DOI":"10.1142\/s0218127418300069","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T05:18:04Z","timestamp":1523510284000},"page":"1830006","source":"Crossref","is-referenced-by-count":2,"title":["Nonchaotic Behavior in Quadratic Three-Dimensional Differential Systems with a Symmetric Jacobian Matrix"],"prefix":"10.1142","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2269-7091","authenticated-orcid":false,"given":"Marcelo","family":"Messias","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia \u2013 FCT\/UNESP, 19060-900 Presidente Prudente, S\u00e3o Paulo, Brazil"}]},{"given":"Rafael Paulino","family":"Silva","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto de Bioci\u00eancias, Letras e Ci\u00eancias Exatas \u2013 IBILCE\/UNESP, 15054-000 S\u00e3o Jos\u00e9 do Rio Preto, S\u00e3o Paulo, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"S0218127418300069BIB001","doi-asserted-by":"crossref","DOI":"10.1007\/b97589","volume-title":"Chaos: An Introduction to Dynamical Systems","author":"Alligood K. 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