We study a multivariate, non-linear Hawkes process ZN on the complete graph with N nodes. Each vertex is either excitatory (probability p) or inhibitory 1?p). take mean-field limit of ZN, leading to multivariate point Z?. If p?12, we rescale interaction intensity by and find that solves deterministic convolution equation all components Z? are independent. In critical case, p=12, N1/2 obtain int...