Mathematical Modeling of Four-dimensional Genetic Regulatory Networks Using a Logistic Function

Mathematical modeling is a universal tool for the study of complex systems. In this paper formulas for characteristic numbers of critical points for the systems of order four (4D) are considered. We show how an unstable focus-focus can appear in a four-dimensional system. Projections of 4D trajectories on two-dimensional and threedimensional subspaces are shown. In the considered four-dimensional system the logistic function is used. The research aims to investigate the four-dimensional system, find critical points of the system, calculate the characteristic numbers, and calculate Lyapunov exponents.