Studying the synchronization of neural networks is crucial for understanding brain function and diagnosing neurological disorders. However, most existing research focuses on integer-order systems and overlooks the effects of time-delay coupling. To address this, this paper was devoted to investigating the synchronization behaviors of time-delay coupled fractional-order FitzHugh–Nagumo networks. The sufficient conditions for the synchronization of two coupled neurons were derived using the Lyapunov stability criterion. Furthermore, the synchronization factor was utilized to elucidate the combined effects of coupling strength and time delay, as well as the influence of time delay on fractional-order dynamics. The analysis began with two coupled systems, and the results were then extended to networks with a larger number of nodes. Numerical examples were presented to illustrate the obtained results.

Neuronal spikes are carriers of neural information, and high-quality recordings are critical for neural coding and brain-computer interface research. However, electrophysiological recordings are often corrupted by noise, reducing the signal-to-noise ratio (SNR) and distorting spike waveforms. Although variational mode decomposition (VMD) is suitable for non stationary neural signal processing, its performance relies heavily on manual selection of mode number $K$ and penalty factor $\alpha$, resulting in poor adaptability. This paper proposes a neuronal spike denoising method combining tornado optimizer with Coriolis force (TOC)-optimized VMD and wavelet thresholding. With Hilbert envelope entropy as the fitness function, TOC adaptively optimizes VMD parameters; the kurtosis criterion separates signal-dominant and noise-dominant components; wavelet thresholding further denoises noise-dominant parts to reconstruct purified spike signals from valid components. Experiments on simulated and real neuronal signals verify that the proposed method outperforms classic empirical mode decomposition, conventional VMD and particle swarm optimization-VMD. Specifically, on real signals, it improves the SNR by 14.0322 dB, reduces mean absolute error by 0.0815 and root mean square error by 0.1102, raises the normalized cross-correlation by 0.0494 and the energy SNR by 6.30%. The proposed method effectively suppresses noise while preserving spike waveform features, providing high-quality data for subsequent spike sorting and neural decoding.