Análise de caos em oscilações de baixa frequência em dispositivos não-lineares

Abstract

In this work we have studied oscillating electronic circuit based on negative differential conductivity (NDC), with possibility to present chaos. The Chua’s circuit was chosen for the nonlinear dynamical and chaotic phenomena studies due to its simple implementation, robustness and easy operation. Its studies have provided important characteristics of NDC devices. Many oscillatory phenomena can be derived by controlling quiescent points of Chua´s circuit I(V) characteristics. This is carried by changing the slope and the position where the load line cross the I(V) characteristics. For this we have carried out two experimental setups, by controlling two distinct parameters of the circuit, namely the series resistance R and the D.C. series voltage with the NDC device (i.e. the Chua diode). We have acquired time series of three circuit points and carried nonlinear dynamical analysis of them. Our analysis considered periodic and chaotic time series depending on the control parameter value for both considered parameters. For the experiments considering the D.C. series voltage source we have obtained a bifurcation diagram which has given information of the structure, sensitiveness to initial conditions and bifurcation types. Such circuit is very stable and low noise and this has permitted us to practice nonlinear dynamical analysis with the computational tools such as Lyapunov spectrum, mutual information, average false nearest neighbors and dimensions like the Kaplan and Yorke, information dimension. Poincaré sections allowed us to obtain bifurcation diagrams and to infer what was the most confident result for the fractal dimension of chaotic attractors.