Charge-balanced time-optimal control for spiking neuron oscillators

In this paper, we investigate the fundamental limits on how the inter-spike time of a neuron oscillator can be perturbed by the application of an external control input (a current stimulus) with zero net electric charge accumulation. We derive the minimum and maximum inter-spike time assignment controls for phase models using the maximum principle, and fully characterize the possible range of neuronal spiking times with respect to a given bound on the control amplitude. We apply the derived optimal controls to both mathematically ideal and experimentally observed phase models of spiking neurons to demonstrate their applicability to neuroscience.