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

The role of intrinsic noise on the spiking of two delay-coupled neurons is studied. ► Characteristic stochastic synchronization patterns are observed. ► The delay-coupling and intrinsic noise result in a locking of the spiking rate. ► The dynamics of the coupled neurons exhibit noise-induced phase-flip bifurcations. 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 for strong channel noise and in turn cause a striking stabilization of the spiking frequency.