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Abstract: In this article, we study optimal control problems of spiking neurons whosedynamics are described by a phase model. We design minimum-power currentstimuli controls that lead to targeted spiking times of neurons, where thecases with unbounded and bounded control amplitude are considered. We show thattheoretically the spiking period of a neuron, modeled by phase dynamics, can bearbitrarily altered by a smooth control. However, if the control amplitude isbounded, the range of possible spiking times is constrained and determined bythe bound, and feasible spiking times are optimally achieved by piecewisecontinuous controls. We present analytic expressions of these minimum-powerstimuli for spiking neurons and illustrate the optimal solutions with numericalsimulations.



Author: Isuru Dasanayake, Jr-Shin Li

Source: https://arxiv.org/







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