LOCAL LARGEST LYAPUNOV EXPONENT IS CRITICAL TO THRESHOLD VOLTAGE AND REFRACTORY PERIODS FOR HODGKIN-HUXLEY MODEL

Abstract

It is not known whether the spike threshold voltage and refractory periods in neocortical neurons reflects the reliability of spike timing underlying mechanisms.  The paper scrutinizes their relationship with local largest Lyapunov exponent (lLLE) in an excitatory Hodgkin-Huxley system under either sinusoidal drive or stochastic Poisson drive.  The influence of the forcing on the response of the system is examined in the realm of suprathreshold amplitudes.  Our results demonstrate that the average lLLE in spike and non-spike regions is different under the physiological threshold voltage and refractory periods.  These dynamics contains:

(i) The average values of the lLLE in spike region are almost negative, and almost positive in non-spike region under sinusoidal driving.

(ii) The values in spike region are nearly constant under sinusoidal drive with varying frequency; however, the values in non-spike region are different.

(iii) Under low Poisson spike rate and different Poisson inputs strength, the average values of lLLE almost remain the same constant in spike and non-spike region.