Study on the critical dynamics of Hodgkin-Huxley neurons with heterogeneous channel coupling under Lévy noise*

Neuronal criticality is crucial for efficient information transmission in the nervous system. However, Gaussian noise fails to replicate the characteristic large-amplitude, low-frequency perturbations of critical states, while existing studies on criticality and ion channel heterogeneity remain confined to single-channel analyses. To address these limitations, we propose an improved Hodgkin-Huxley (HH) neuron model that integrates Lévy noise with multi-channel heterogeneity to investigate critical dynamics. On the noise scale, a non-Gaussian noise-driven HH neuron model is constructed by simulating the nonlinear effect of the heavy tail characteristics of Lévy noise and the nonlinear effect of ion channel heterogeneity on membrane potential; on the ion channel scale, a cross-scale correlation model of microscopic heterogeneity and macroscopic discharge mode is constructed by combining the conductance proportional scaling coefficient of sodium and potassium channels; finally, a multi-dimensional parameter spatial thermal map and three-dimensional distribution are introduced, and multi-parameters are fused to construct a phase change analysis model. Experiments show that when the sodium-potassium conductivity ratio exceeds 1.25, neurons jump from resting state to high-frequency discharge, and the coupling effect of Lévy noise to the sodium-potassium conductivity ratio significantly promotes the discharge behavior of neurons under low current conditions. The noise-heterogeneity-input coupling model constructed in this paper provides a new idea for the functional coordination of randomness and heterogeneity in neural information encoding, and has potential application value in the analysis of pathological abnormal discharge mechanisms and neural network optimization.