Computing Equilibrium Points of Genetic Regulatory Networks

Computing equilibrium points of genetic regulatory networks is a problem of primary importance for numerous investigations in these systems. This paper addresses this problem for differential equation models, with the regulation function expressed in a general form which includes both SUM form and PROD form for saturation functions of any type. Specifically, a recursive algorithm is proposed, which provides at each recursion a region guaranteed to contain all equilibrium points. This region progressively shrinks, and asymptotically converges to the sought set of equilibrium points. Moreover, the proposed algorithm can also allow one to delimit and find limit cycles. Some numerical examples are reported to illustrate and validate the proposed algorithm, including examples where standard mathematical tools fail to compute the sought equilibrium points.