Identifying dyssynchronous states in FitzHugh-Nagumo neuronal network excited by local Lévy noise using reservoir computing

Yanming Liang, Yongfeng Guo, Zifei Lin and Tomasz Kapitaniak

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: Chimera states, characterized by the coexistence of synchronized and desynchronized regions within oscillator networks, have been increasingly linked to the abnormal spatiotemporal dynamics observed in neurological disorders such as epilepsy and Parkinson's disease. However, conventional modeling approaches often rely on deterministic frameworks or Gaussian white noise with uniform distributions, which inadequately capture the localized and asymmetric features of pathological neural events, such as focal seizure onset and dopaminergic imbalance. In this study, we propose a biologically inspired modeling framework based on a non-locally coupled FitzHugh-Nagumo (FHN) neuronal network subjected to localized Lévy noise. This framework offers a more realistic representation of pathological brain activity. The heavy-tailed and skewed characteristics of Lévy noise effectively simulate the burst-like, intermittent discharges typical of epileptic foci, as well as the asymmetric firing patterns observed in Parkinsonian basal ganglia circuits. To address the limitations of traditional numerical solvers in capturing such complex, noise-driven dynamics, we introduce a deep learning-based solver that integrates short-term memory and global signal dependency modeling. This method significantly enhances computational accuracy, generalization, and robustness, especially under strong non-Gaussian perturbations. In particular, we demonstrate that reservoir computing algorithms are highly effective in identifying dynamic states within coupled neuronal networks. Our results reveal the emergence of diverse chimera patterns across varying Lévy noise parameters, highlighting transitions from globally synchronized states to localized seizure-like activity or widespread chaotic regimes. These findings establish a mechanistic and computational link between deep learning and neurodynamics, offering new insights into the early propagation of seizures and disruptions in Parkinsonian networks.

Keywords: Reservoir computing; Lévy noise; FitzHugh-Nagumo neuronal network; Neurological disorders (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014973

DOI: 10.1016/j.chaos.2025.117484

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