Unified Entropy–Spectral Fingerprinting of Chaotic Attractors via CFS, Lyapunov Stability, and Nonlinear Complexity Measures

Chaotic dynamical systems, such as the Lorenz, Rössler, and Duffing attractors, are studied for their irregular trajectories and broadband spectra. However, a unified framework for their fingerprinting and quantitative measures is not widely present. Existing methods focus on either spectral methods or dynamical complexity measures in isolation, which limits interpretability and robustness across diverse regimes. In this work, we propose an entropy based spectral fingerprinting framework that integrates the Characteristic Frequency Score (CFS) obtained from short time Fourier transform (STFT) and Continuous Wavelet Transform (CWT) with nonlinear complexity metrics including the largest Lyapunov exponent (LLE), approximate entropy (ApEn), and permutation entropy (PermEn). Using clean signal analysis, we show that the Duffing oscillator produces compact spectral concentration with high instability and low entropy, the Lorenz system exhibits broadband spreading with higher entropic complexity, and the Rössler attractor displays intermediate behavior. Confidence intervals which are derived through bootstrap resampling confirm the statistical stability of the extracted measures, with STFT emphasizing global spectral spread and CWT highlighting localized structures. The proposed framework offers an interpretable and statistically consistent means of fingerprinting chaotic systems, with applications in secure communication, biomedical signal monitoring, fault diagnostics, and complexity science.