On the Noise-Enhancing Ability of Stochastic Hodgkin-Huxley Neuron Systems

Recently noise has been shown to be useful in enhancing neuron sensitivity by stochastic resonance. In this study, in order to measure the noise-enhancing factor (NEF), a nonlinear stochastic model is introduced for the Hodgkin-Huxley (HH) neuron system with synaptic noise input stimulation and channel noises in the sodium and potassium channels. The enhancing factor of the HH neuron system is measured from the point of view of the noise-exploiting level of nonlinear stochastic H∞ signal processing. Since the nonlinear stochastic-enhancing measure problem of HH neuron systems requires a solution for the difficulty presented by the Hamilton Jacobi inequality (HJI), a fuzzy interpolation of locally linearized systems is employed to simplify the nonlinear noise-enhancing problems by solving only a set of linear matrix inequalities. The NEF of the HH neuron system is found to be related to the locations of eigenvalues of linearized HH neuron systems and can be estimated through the H∞ signal processing method. Based on a stochastic fuzzy linearized HH neuron system, we found that channel noises are enhanced by the active eigenvalues of ionic channels while synaptic noises are attenuated by the passive eigenvalues of synaptic process.