In this work we do an approach on non-linear dynamical systems in non-linear systems that behave or not in a chaotic way. The objective of this work is observe the dynamic of the chosen systems by the use of mathematical simulations, for more complete studies. The utilized concepts treats denitions about phase space, dissipative systems, attractors, equilibrium solutions, linear stability in two dimensions, limit cycles, bifurcations and the calculation of the Lyapunov exponents. The data acquisition was made through academic research in books, articles and dissertations of interest and, as well, the Maple, Maxima and Mathematica softwares which were very useful to the development of the calculations and the graphic plots utilized in this present work, principally in the applications. We expect that other works could be developed from this to complement the existing studies in this area, acting as support for more researches.
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