Fluid Neural Networks (FNN) are a mathematical framework where the phenomenon of self-synchronization in ant colonies can be explained, predicting the model a critical density, i.e. a density where oscillations appear, observed in real ant colonies. However, up to now all results have been solely numerical. In this paper we put forward a simpler FNN with the same phenomenology as the original one, but an analytical approximation can be performed in such a way that critical densities can be computed, offering a good approximation to the numerical ones.