Single input optimal control for globally coupled neuron networks

We consider the problem of desynchronizing a network of synchronized, globally (all-to-all) coupled neurons using an input to a single neuron. This is done by applying the discrete time dynamic programming method to reduced phase models for neural populations. This technique numerically minimizes a certain cost function over the whole state space, and is applied to a Kuramoto model and a reduced phase model for Hodgkin-Huxley neurons with electrotonic coupling. We evaluate the effectiveness of control inputs obtained by averaging over results obtained for different coupling strengths. We also investigate the applicability of this method to Hodgkin-Huxley models driven by multiplicative stimuli.