DETECTING AND STABILIZING PERIODIC ORBITS OF CHAOTIC HENON MAP THROUGH PREDICTIVE CONTROL
The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.
I , as main author, declare and undersign, that the paper is an original and common work of me and all subsequent authors. The paper as a whole or part of it has not been published or submitted to other Journal. The right to publish the accepted paper is transferred to and owned by “Annals of Constanta Maritime University” Journal.