Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise

Details Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise

2012-02-12

arxiv.org/abs/1202.2491v1

Biology

Quantitative Biology

Neurons and Cognition

27 pages, 16 figures

Scientific paper

In previous articles we have investigated the firing properties of the standard Hodgkin-Huxley (HH) systems of ordinary and partial differential equations in response to input currents composed of a drift (mean) and additive Gaussian white noise. For certain values of the mean current, as the noise amplitude increased from zero, the firing rate exhibited a minimum and this phenomenon was called inverse stochastic resonance (ISR). Here we analyse the underlying transitions from a stable equilibrium point to the limit cycle and vice-versa. Focusing on the case of a mean input current density $\mu=6.8$ at which repetitive firing occurs and ISR had been found to be pronounced, some of the properties of the corresponding stable equilibrium point are found. A linearized approximation around this point has oscillatory solutions from whose maxima spikes tend to occur. A one dimensional diffusion is also constructed for small noise based on the correlations between the pairs of HH variables and the small magnitudes of the fluctuations in two of them. Properties of the basin of attraction of the limit cycle (spike) are investigated heuristically and also the nature of distribution of spikes at very small noise corresponding to trajectories which do not ever enter the basin of attraction of the equilibrium point. Long term trials of duration 500000 ms are carried out for values of the noise parameter $\sigma$ from 0 to 2.0, with results appearing in Section 3. The graph of mean spike count versus $\sigma$ is divided into 4 regions $R_1,...,R_4,$ where $R_3$ contains the minimum associated with ISR.

Affiliated with

Also associated with

No associations

Rating

Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analysis of inverse stochastic resonance and the long-term firing of Hodgkin-Huxley neurons with Gaussian white noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-371454