Genetic Networks with SUM Regulatory Functions: Characterizing the Equilibrium Points

Genetic networks with SUM regulatory functions are a fundamental class of models studied in systems biology. A primary issue for these models consists of establishing the number of the equilibrium points and their location. Unfortunately, this is a difficult problem, indeed existing methods very often do not allow one to solve it. This paper proposes a study of this problem, and describes an approach that exploits the properties of SUM regulatory functions in order to correctly characterize these points of interest. This is verified by some numerical examples, which illustrate the proposed solution and show the advantages with respect to existing methods.