Stochastic neural dynamic modeling and analysis under environmental noise for exploring the production of K-complexes

K-complexes (KCs), sleep-specific neuroprotective waveforms, demonstrate significant modulation by environmental noise (EN). However, the principles governing how EN modulates KCs occurrence remain poorly understood. To address this gap, we develop a stochastic neural dynamic model incorporating EN (SNDM-KCs) and explore the modulation effects of EN on KCs from the perspective of stochastic dynamics. The Gaussian colored noise (GCN) is first applied to model EN and introduced into the deterministic Costa neural mass model to build the SNDM-KCs. Next, bifurcation analysis is conducted to demonstrate that the prerequisite for occurrence of KCs corresponds to a large-amplitude departure from a stable equilibrium induced by GCN in the dynamic system. Subsequently, we study the impact of GCN on KCs by integrating SNDM-KCs with defined two metrics to quantitatively measure the elicitation variation of KCs. Numerical simulations suggest that both KCs occurrence probability and rate increase with noise intensity D and correlation rate [Formula: see text] of GCN. Meanwhile, building on stochastic escape theory, we establish the relationship between model behaviour and stochastic escape metrics: first escape probability (FEP) and the mean first exit time (MFET), to investigate how EN modulates KCs through the lens of stochastic dynamics. The results demonstrate that as the escape probability of the system rises, the occurrence probability of KC increases accordingly. Meanwhile, a shorter time to escape from the safe domain indicates a faster occurrence rate of KCs. Our work provides a novel dynamical insight for investigating the principles governing how EN modulates KCs occurrence.

The online version contains supplementary material available at 10.1007/s11571-026-10440-4.