Control of Collective Bursting in Small Hodgkinhuxley Neuron Clusters

Abstract

The speed gradient-based control algorithm for tracking the membranepotential of Hodgkin-Huxley neurons is applied to their small clusters modeling thebasic features of an epileptiform dynamics. One of the neurons plays a role of controlelement detecting the temporal hyper-synchronization among its network companionsand switching their bursting behavior to resting. The ‘toy’ model proposed in thepaper can serve as an algorithmic basement for developing special control elements atthe scale of one or few cells that may work autonomously and are able to detect andsuppress epileptic behavior in the networks of real biological neurons.