Mean field game problem for the optimal control of neuronal spiking activity
Optimization and Control
2024-12-18 v1
Abstract
We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large.
Keywords
Cite
@article{arxiv.2412.12682,
title = {Mean field game problem for the optimal control of neuronal spiking activity},
author = {Lijun Bo and Dongfang Yang and Shihua Wang},
journal= {arXiv preprint arXiv:2412.12682},
year = {2024}
}