Optimal Design of Minimum-Power Stimuli for Spiking Neurons

TL;DR

This paper develops optimal control strategies to design minimum-power stimuli for spiking neurons modeled by phase dynamics, considering both bounded and unbounded control amplitudes, with analytic solutions and numerical validation.

Contribution

It introduces analytic expressions for minimum-power stimuli in phase-model neurons, addressing bounded and unbounded control cases with optimal control theory.

Findings

Unbounded control allows arbitrary spiking period modification.

Bounded control constrains spiking times within a feasible range.

Analytic solutions effectively generate minimum-power stimuli.

Abstract

In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking times of neurons, where the cases with unbounded and bounded control amplitude are considered. We show that theoretically the spiking period of a neuron, modeled by phase dynamics, can be arbitrarily altered by a smooth control. However, if the control amplitude is bounded, the range of possible spiking times is constrained and determined by the bound, and feasible spiking times are optimally achieved by piecewise continuous controls. We present analytic expressions of these minimum-power stimuli for spiking neurons and illustrate the optimal solutions with numerical simulations.