Abstract: The aim of the present work is to identify a connection network describing the expression profiles of the genes involved in the cellular cycle of the yeast. In order to derive such connections from the microarray data, a mathematical model is needed, whose states represent the expression levels of the genes. However, since the cellular dynamics exhibit a limit cycle behavior [1] (i.e. roughly speaking, a periodic response, which is robust to small perturbations), it is not possible to describe the whole phenomenon by means of only linear models. Therefore, we investigate the suitability of quadratic systems [2], for the description of the genetic network dynamics. A quadratic system is made up of a set of first order differential equations, with linear terms plus quadratic terms (i.e. multiplications between two state variables or between a state and an input variable).