Multi-chaotic signal identification employing a causal cross-correlation neural network

Chaos identification plays a crucial role in comprehending complex systems. However, current methods face three challenges: neglect temporal causality, lack robustness against noise, and identify a limited number of chaotic signals. To address the challenges, we focus on identifying multi-chaotic signals with noise interference. First, this study examines 15 types of chaos models. We propose an acquisition-enhanced Bayesian optimization to improve the Swish-modulo map, which is then verified using the maximum Lyapunov exponent. Second, we present a causal cross-correlation network for chaos identification, which incorporates a learnable wavelet transform, time-frequency feature fusion, and spectral-inversion-free fast Fourier transform-based cross-correlation (SFFT-CC). Consequently, experimental results show that the chaos identification accuracy reaches 96.67% at a 20 dB noise. The SFFT-CC outperforms the traditional dilated convolution by up to 5.42% in chaos identification accuracy, while achieving a 43-fold reduction in training time. Theoretical analyses are provided to elucidate these results.