A framework for chaotic signature classification: Insights from Chua’s circuit

In this preliminary work we investigate the possibility to extract, from the analysis of a chaotic signal, a signature of the circuit that generated it. It is widely known that even small deviations in parameters of a chaotic circuit are reflected into generated signals with different dynamics and characteristics, not detectable by simple inspection and impossible to reproduce in another circuit. Being able to identify these differences, and being also able to verify if a sequence has been effectively generated by a given circuit will pave the way to new applications of chaotic circuits including, but not limiting to, security applications. In this paper we consider Chua’s circuit, that is one of the simplest known chaotic circuits, and we show that by using deep learning and time-frequency transformations it is possible to extract a signature from chaotic sequences. Results are provided using two simulated datasets, and also two experimental datasets acquired from six hardware realizations of Chua’s circuit. All signals are transformed into Short-Time Fourier Transform and classified with Convolutional Neural Network (CNN) models, achieving 98% macro-averaged balanced accuracy across the evaluated test sets, including 224 distinct chaotic parameterizations, unveiling a data-driven route to fingerprint chaos. As additional results, gradient-based interpretability and Permutational Multivariate Analysis of Variance (PERMANOVA) based statistical analysis are provided to support distinctive time-frequency features of the signatures.