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