Estudo de sistemas dinâmicos não lineares

Abstract

In this work we present a study on nonlinear dynamical systems and the qualitative and quantitative process to find the solutions of their governing equations. We found approximate numerical solutions using the fourth-order Runge-Kutta algorithm. We apply machine learning methods to find and predict the system’s behavior from the data collected about it, assuming that its governing equation was not yet known. The methods used were the Ridge and Lasso regressions which present a regularization term on the coefficients that govern the equations of motion. We apply all these mechanisms in the Lorenz equations. We obtain by the fourth order Runge-Kutta the approximate solutions and the behavior through the governing equations and the initial parameters; through regressions we obtain the behavior and produce predictions from the data set of velocities and states collected in the system. We conclude that the regressions used approached the behavior predicted by the literature but were not enough to extract the exact coefficients that accompany the governing equations of the system in such a way as to identify them.