Describing function based analysis of the characteristics of chaotic behavior in the jerk dynamic system

The study of nonlinear dynamic systems that may have chaotic behavior has been an investigation field of interest in recent years. Deeper analysis of methods to find chaotic patterns in nonlinear systems has been done; however, these methods are complex and require exhaustive data analysis. The describing function method hasn't been associated much to the dynamics of chaos. This method provides useful information of the oscillatory behavior of a system, in a more direct and simple way. It is for this reason that this article bases the analysis of a classical chaotic system, on the describing function method. First an analysis over a group of nonlinear functions that generate chaotic behavior in the jerk system is performed, these functions have different characteristics from each other, allowing assess the most plausible scenarios in the dynamic system. Then a mathematical tool for the analysis of chaos in the frequency domain is presented through the describing function. Finally the results obtained by the analysis of the describing function are shown and checked with simulations.