Gompertz function in the model of gene regulatory networks

We examine a network model (including gene regulatory networks), which consists of a system of two ordinary differential equations. This system contains several parameters and depends on the regulatory matrix, which describes interactions in this two-component network. We consider attracting sets of the system, which vary depending on the parameters and elements of the regulatory matrix. Our considerations are of geometric nature, which allows us to identify and classify possible interactions in the network. The system of differential equations contains a sigmoidal function, which makes it possible to take into account peculiarities of the network's response to external influences. The Gompertz function was chosen as the sigmoidal function, which allows us to compare the results with similar results for models of two-component networks based on the logistic sigmoidal function.