Multiwavelet and multiwavelet packet analysis in qualitative assessment of the chaotic states

This article demonstrates the application of multiwavelet analysis and multiwavelet packet analysis in qualitatively assessing the chaotic nature of a system’s response. Ranges of model parameters that induce chaotic behavior are identified, and the system’s response under these conditions is then analyzed using multiwavelet analysis and multiwavelet packet analysis. By employing a one-degree-of-freedom nonlinear system as an illustrative example, the transition from a non-chaotic to a chaotic state is shown to affect both the magnitude and the temporal distribution of wavelet coefficients across multiple levels of the response analysis. The cumulative energy of the signal’s multiwavelet approximation is calculated to distinguish between chaotic and non-chaotic signals. The results obtained through multiwavelet analysis in identifying the system’s critical states are compared with those derived from traditional wavelet analysis and other established methods for assessing chaos. The presented approach is an alternative to other methods of qualitative identification of chaotic states, and also to provide a generalization to the method in analyzing complex systems.