Genetic engineering – construction of a network of four dimensions with a chaotic attractor

Abstract

Systems of ordinary differential equations (ODE) of special form are considered in this paper. These systems appear in various models of genetic regulatory networks and telecommunication networks. The model of a genetic network with a chaotic attractor of dimension four is constructed. Geometrical considerations are used to study the properties of the systems. Computation of Lyapunov exponents is used to prove the existence of chaotic attractors. Problems of control and management of such regulatory systems are challenging issues in the theory of genetic networks.