Limits and dynamics of randomly connected neuronal networks

TL;DR

This paper investigates how random connectivity and delays in large neuronal networks influence their collective dynamics, deriving mathematical limits and demonstrating the impact of network architecture on activity patterns.

Contribution

It provides a rigorous analysis of the mesoscopic and macroscopic limits of randomly connected neuronal networks with delays, including new solvable models and insights into periodic activity emergence.

Findings

Propagation of chaos in large networks

Convergence to McKean-Vlasov equations with delays

Connectivity influences periodic solutions

Abstract

Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these random architectures on the dynamics of such networks, we analyze the mesoscopic and macroscopic limits of networks with random correlated connectivity weights and delays. We address both averaged and quenched limits, and show propagation of chaos and convergence to a complex integral McKean-Vlasov equations with distributed delays. We then instantiate a completely solvable model illustrating the role of such random architectures in the emerging macroscopic activity. We particularly focus on the role of connectivity levels in the emergence of periodic solutions.