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Chaotic Dynamics of a Nonlinear Electronic converter

The nonlinear electronic converter used by Rulkov and collaborators [Rulkov et al., 2001], which is the core of their chaotic oscillator, is modeled and simulated numerically by means of an appropriate direct relationship between the experimental values of the electronic components of the system and the mathematical model. This relationship allows us to analyze the chaotic behavior of the model in terms of a particular bifurcation parameter k. Varying the parameter k, quantitative results of the dynamics of the numerical system are presented, which are found to be in good agreement with the experimental measurements that we performed as well. Moreover, we show that this nonlinear converter belongs to a class of 3-D systems that can be mapped to the unfolded Chua's circuit. We also report a wavelet transform analysis of the experimental and numerical chaotic time series data of this chaotic system. The wavelet analysis provides us with information on such systems in terms of the concentration of energy which is the standard electromagnetic interpretation of the L2 norm of a given signal.