Modeling Systems Based on the Assessment of Weak Symmetry Breaking in Reconstructed Attractors

Abstract

The paper proposes to use the research method for chaotic processes based on the identification of weak symmetry breaking of the restored attractor. It is shown how the calculations results can be used to identify systems. An algorithm for creating finite-difference models has been developed, including: calculating by numerical methods the necessary conditions for the existence of chaos, reconstructing an attractor in a time series, searching for symmetric attractor fragments under conditions of weak symmetry breaking, determining the form of nonlinearities, and parametric identification. The result of the algorithm is a system of finite-difference equations in the state space Criteria for assessing symmetry breaking based on estimates of the divergence of fragments of phase trajectories are introduced. The results of modeling systems with chaotic dynamics are presented.