Poly-Gaussian description of probability distributions of processes generated by a nonlinear Lorenz system implemented in fixed-point numbers

The article is aimed at analyzing the probability distributions of pseudorandom processes generated on the basis of the Lorentz system solution in fixed-point numbers. Numerical solution of the Lorenz system by the Euler method in single- and double-precision floating-point numbers with a limited number capacity can lead to a breakdown in signal generation. The use of fixed-point numbers contributes to the reduction of computational complexity in the digital implementation of such systems, which ultimately leads to the simplification of their practical implementation on modern chips of programmable logic. This allows to use resources in more efficient way, and increases productivity in the creation and maintenance of such digital systems. The study of approximation of Lorenz system signals using mixtures of Gaussian distributions is of great importance for predictive analytics and stability of the system. Elimination of signal generation failure also contributes to the formation of stable modes of generation of chaotic signals with required statistical characteristics.