The Bifurcation Coalescence Problem for Feedforward Coalescence Networks

Consider two networks and combine them through the coalescence operation to get a larger network. Is it possible to study the steady-state bifurcations of the coalescence network by studying the steady-state bifurcations of the component networks? We conclude that this is not possible for general coalescence networks. We show, however, that in the case of feedforward coalescence networks this is possible and we cover the simplest cases. In particular, we prove how the growth rate of the bifurcation branches in the feedforward coalescence network depends on the connections from one network to the other.