Wavelet-Based Detection of Strange Nonchaotic Attractors

Strange nonchaotic attractors (SNA) are fractal invariant sets characterized by aperiodic dynamics and nonpositive largest Lyapunov exponents. Due to the fractal geometry and the absence of exponential sensitivity to initial conditions, SNA are often difficult to distinguish from chaotic attractors using time-series data. This study examines the applicability of wavelet-based analysis for the detection of strange nonchaotic regimes in dynamical systems. The proposed approach involves the analysis of wavelet scalograms and global wavelet energy spectra. It is shown that quasiperiodic and strange regimes can be distinguished by the structure of their scalograms. To distinguish between strange nonchaotic and chaotic regimes, global wavelet energy spectra are employed. Numerical results demonstrate the applicability of this method for identifying quasiperiodic, strange nonchaotic, and chaotic regimes from time-series data.