Modelamiento, Simulación e Implementación Del Oscilador Por Medio De La Ecuación De Duffing

Abstract

The article presents the research that led to the observation, modeling and analysis of a chaotic oscillator determined by the Duffing equation: x ̈+ εx ̇-βx+αx^3=f Cos⁡(wt) obtained when a muffled and forced movement occurs and also the description of three solutions: the approximate analytical, physics and simulated. In this case, the system is mathematically modeled by a differential equation ordinary of second order non linear – or its respective representation as a differential equation system -. The Method of “Runge-Kutta” is applied for the solutions of the equations system, the numerical method of “Adomian decomposition” (ADM) is adopted by its implementation in MatLab R in order to provide the approximated solution to the equation, as well as the solution thrown after the implementation of the associated circuit. The chaos presence is confirmed making use of the Exponents of Lyapunov. Finally both, the output variables and the phase diagram generated were analyzed. Making the comparison between the obtained solutions by Runge-Kutta, the simulated and the one shown by the circuit design adopted.