Area aggregation and time-scale modeling for sparse nonlinear networks

Model reduction and aggregation are of key importance for simulation and analysis of large-scale systems, such as molecular dynamics, large swarms of robotic vehicles, and animal aggregations. We study a nonlinear network which exhibits areas of internally dense and externally sparse interconnections. The densely connected nodes in these areas synchronize in the fast time-scale, and behave as aggregate nodes that dominate the slow dynamics of the network. We first derive a singular perturbation model which makes this time-scale separation explicit and, next, prove the validity of the reduced-model approximation on the infinite time interval.