Моделирование и управление хаотическим процессом

Abstract

The article investigates problems related to the control of the dynamics of a system given by the Henon map with a hysteresis component included in it. In particular, possible modifications of the limit set (attractor) of the modified Henon map under hysteresis conditions are studied. The hysteresis element is formalized based on design approach by means of the Preisach model, which is approximated by a system consisting of a finite set of non-ideal relays. To analyze the dynamics, numerical simulation is carried out for various values of the model parameters, which are characterized by chaotic dynamics. For this purpose, a Python script has been developed that simulates the dynamics of the system under hysteresis conditions, and also processes the results to identify dynamic modes. Based on the data obtained, a comparative analysis of strange attractors of the modified and classical Henot mappings is carried out. Next, we study the dynamics depending on the parameters of the modified Henon map. To detect various dynamic regimes, bifurcation diagrams were plotted, the high Lyapunov exponent was calculated based on the Rosenstein algorithm and the 0-1 test was produced depending on the system parameters, and the hysteresis nonlinearity parameter. Established, that hysteresis term regularize dynamics of the system compared to the classical map and changed in the position of bifurcation points in the space of system parameters.