Search

This work introduces a new six-dimensional system with chaotic and periodic solutions. For special values of parameters, we calculate the Kaplan-Yorke dimension and we show the dynamics of Lyapunov exponents. Some definitions and propositions are given. Visualizations where possible, are provided.

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.

We consider the three-dimensional gene regulatory network (GRN in short). This model consists of ordinary differential equations of a special kind, where the nonlinearity is represented by a sigmoidal function and the linear part is present also. The evolution of GRN is described by the solution vector X(t), depending on time. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way.