Various types of recurrent neural networks have been used as models for the regulatory relationships between genes. The neural network is trained on the data from micro-array techniques, each gene corresponds to a neuron in the network. The data from the micro-array technologies has numerous genes, but usually involves few samples, this makes the network heavily under-determined. In this work we will propose a method that can cope with the poorness of the data. We will use a Hopfield-type neural network to model the ontogenetic differentiation of female honeybees. A method that identifies the genes that determine the castes is proposed.