Control and Synchronization of Neuron Ensembles

TL;DR

This paper investigates controlling and synchronizing ensembles of neuron oscillators using phase models, deriving optimal controls analytically and computationally, with applications in neuroscience and engineering.

Contribution

It introduces a universal control methodology for nonlinear phase oscillators, including analytical solutions and pseudospectral computational methods for neuron ensembles.

Findings

Analytical optimal controls for single and two-neuron systems.

Applicability of controls to large neuron ensembles.

A robust pseudospectral method for optimal neuron control.

Abstract

Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems. Controlling synchronization of oscillating systems is motivated by a wide range of applications from neurological treatment of Parkinson's disease to the design of neurocomputers. In this article, we study the control of an ensemble of uncoupled neuron oscillators described by phase models. We examine controllability of such a neuron ensemble for various phase models and, furthermore, study the related optimal control problems. In particular, by employing Pontryagin's maximum principle, we analytically derive optimal controls for spiking single- and two-neuron systems, and analyze the applicability of the latter to an ensemble system. Finally, we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations. The methodology developed here is universal to the control of general nonlinear phase oscillators.