In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons

TL;DR

This study explores how intrinsic channel noise affects delay-coupled Hodgkin-Huxley neurons, revealing robust stochastic synchronization patterns with phase-flip bifurcations that stabilize spiking frequency.

Contribution

It introduces a stochastic Hodgkin-Huxley model with delay-coupling to analyze noise effects on neuronal synchronization and phase-flip bifurcations.

Findings

Detection of stochastic synchronization patterns with phase-flip bifurcations

Robustness of phase-flips under strong channel noise

Stabilization of spiking frequency due to phase-flips

Abstract

We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust in strong channel noise and in turn cause a striking stabilization of the spiking frequency.