Before revision:  It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic rate functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure.
After revision:  It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic intensity functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure.