A Numerical-Analytical Method for Constructing Periodic Solutions of the Lorenz System

Abstract: This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form concerning of the cyclic frequency, constant terms and amplitudes of harmonics that make up harmonic approximations to the desired solutions. The initial approximation for the Newton method is selected, which converges to a solution describing a periodic solution different from the equilibrium position. The results of a computational experiment are presented. The results are verified using high-precision calculations.