Synchronization in Networks with Nonlinearly Delayed Couplings on Example of Neural Mass Model

TL;DR

This paper analyzes synchronization in networks with nonlinear delayed couplings, applying the circle criterion to neural mass models, and provides stability conditions supported by simulations.

Contribution

It introduces a new approach using mean-field dynamics and the circle criterion to establish synchronization stability in neural networks with nonlinear delays.

Findings

Derived stability conditions for neural mass network synchronization.

Applied the circle criterion to delayed diffusive couplings.

Validated results through simulations.

Abstract

The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem of network synchronization is reduced to the studying of synchronization-error system stability. The circle criterion for time-delay systems is used to derive the stability conditions of synchronization-error system. Obtained results are applied to a network of neural mass model populations, and the synchronization conditions are established. Simulation results are provided to illustrate the obtained analytical results.