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Bifurcation Chaos"],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> In this paper, we report results related with the dynamics of two discrete-time mathematical models, which are obtained from a same continuous-time Brusselator model consisting of two nonlinear first-order ordinary differential equations. Both discrete-time mathematical models are derived by integrating the set of ordinary differential equations, but using different methods. Such results are related, in each case, with parameter-spaces of the two-dimensional map which results from the respective discretization process. The parameter-spaces obtained using both maps are then compared, and we show that the occurrence of organized periodic structures embedded in a quasiperiodic region is verified in only one of the two cases. Bifurcation diagrams, Lyapunov exponents plots, and phase-space portraits are also used, to illustrate different dynamical behaviors in both discrete-time mathematical models. <\/jats:p>","DOI":"10.1142\/s0218127419501426","type":"journal-article","created":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T05:04:31Z","timestamp":1569301471000},"page":"1950142","source":"Crossref","is-referenced-by-count":18,"title":["Nonlinear Dynamics of Two Discrete-Time Versions of the Continuous-Time Brusselator Model"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2235-0469","authenticated-orcid":false,"given":"Paulo C.","family":"Rech","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"S0218127419501426BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.05.036"},{"key":"S0218127419501426BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.055204"},{"key":"S0218127419501426BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.01.018"},{"key":"S0218127419501426BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.03.022"},{"key":"S0218127419501426BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2012.02.036"},{"key":"S0218127419501426BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.09.020"},{"key":"S0218127419501426BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s10910-018-0931-4"},{"key":"S0218127419501426BIB008","volume-title":"The Golden Ratio and Fibonacci Numbers","author":"Dunlap R. 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