Wavelet Resolution Analysis of State Variables in a Double-Scroll Chaotic Attractor

Abstract

This work investigates the distribution of signal energy across resolution levels for the three state variables (x1, x2, x3) of the double-scroll attractor using discrete wavelet transforms. The analysis identi es, for each state, the resolution levels that concentrate the largest fraction of the signal energy, thus revealing which variables and scales are most informative for reconstructing the chaotic trajectory. The results show that the states di er in their energy localization, suggesting variable-speci c roles in encoding the system’s dynamics. Although this study is limited to the double-scroll con guration, we hypothesize that in multi-scroll chaotic systems, the state directly responsible for scroll generation may exhibit a broader, possibly fractal-like, energy distribution, while other states remain more concentrated in a small set of resolution levels. This insight opens the possibility of e cient state selection and scale targeting for chaotic signal recovery, masking, or feature extraction in future work.