Desynchronization effects of a current-driven noisy Hindmarsh-Rose neural network

We investigate the effects of an external current in a disordered Hindmarsh-Rose neural network. The external bias appears in the Hindmarsh-Rose equations as either a noise term (identical or not for all elements), or a sinusoidal drive with a phase delay between the neural units. The Hindmarsh-Rose units inside the network are non-identical and they are coupled through electrical synapses, which allow a gap junction. Measuring synchronization through the Kuramoto order parameter, that is sensitive to the synchronization among the units rather than to the regularities of the trajectories, one finds that common noise induces synchronization, while the distributed noise, as well as the distributed sinusoidal drive, can desynchronize the network. The dynamics of the neural units shows that the bursting behavior is systematically and progressively replaced by a firing activity that becomes similar to the form of the external current. Deep modifications of the single firing dynamics and of the synchronization between the units, systematically occur for a critical value of the control parameters, either the coupling strength, the external drive amplitude, or the noise intensity. We emphasize the desynchronization effect of an external current, an effect that can be relevant for epileptic seizures provoked by network synchronization. The objective of this comparison between different perturbations for the same network is to seek for possible indications of the most effective mean to induce desynchronization.