Henon map with hysteresis: chaos control

Abstract

The article investigates the dynamics of the system, given by the Henon map with hysteresis term. The hysteresis element is formalized based on design approach. The paper investigates a problem of the dynamic control of such system. In particular, possible modifications of the limit set (attractor) of the modified Henon map are studied. Dynamics of the system analyzed through the numerical simulations carried out for various values of the parameters, which are characterized by chaotic dynamics. The comparative analysis between classical Henon map and modified ones are given based on obtained data. To detect various dynamic regims, bifurcation diagrams were ploted, 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.