A Noisy Multi-Agent Framework for the Dynamics of Interacting Neurons

This work investigates the collective behavior of neuronal populations through a stochastic multi-agent framework that models neurons as particles subject to noise in both the membrane voltage evolution and the interactions between neurons. Employing tools from stochastic calculus and measure theory, the study derives macroscopic equations that describe the mean-field dynamics of the system. These approximations enable a rigorous characterization of large-scale neural activity, including conditions for synchronization and stability in the presence of noise. The mathematical formulation is highly general, can be grounded in biologically plausible assumptions to offer insights into how local fluctuations can influence global patterns of brain dynamics. Potential applications include modeling cortical connectivity and analyzing neural variability observed in neuroimaging data. This approach establishes a formal link between microscopic neuronal interactions and emergent macroscopic behavior, providing a valuable analytical tool for theoretical neuroscience and the study of brain function under uncertainty.