2024/12/17 by Lijun Bo, Dongfang Yang, Bo, Lijun +3
Computer Science · Engineering · #Neural Networks Stability and Synchronization #Stability and Control of Uncertain Systems #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2412.12682
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.