Abstract
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.
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