Mathematical Modeling of Three - Dimensional Genetic Regulatory Networks Using Logistic and Gompertz Functions

Abstract

Mathematical modeling is a method of cognition of the surrounding world in which the description of the object is carried out in the language of mathematics, and the study of the model is performed using certain mathematical methods. Mathematical models based on ordinary differential equations (ODE) are used in the study of networks of different kinds, including the study of genetic regulatory networks (GRN). The use of ODE makes it possible to predict the evolution of GRN in time. Nonlinearity in these models is included in the form of a sigmoidal function. There are many of them, and in the literature, there are models that use different sigmoidal functions. The article discusses the models that use the logistic function and Gompertz function. The comparison of the results, related to three-dimensional networks, has been made. The text is accompanied by examples and illustrations.