Computational chaos control based on small perturbations for complex spectra simulation

Abstract

In this paper, we propose to use a computational method of chaos control to simulate complex experimental spectra. This computational chaos control technique is based on the Ott–Grebogi–York (OGY) method. We chose the logistic map as the base mathematical model for the development of our work. For the numeric part, we created arbitrary precision algorithms to generate the solutions. This way, we completely eliminated any degradation of chaos from our results. These algorithms were also necessary for the proper perturbation process that the computational chaos control method requires. We control the chaos of the logistic map in two cases of Period 1 and one case of Period 2 to demonstrate that our control method works. The behavior of a complex experimental spectrum was taken and numerically simulated. The simulated spectrum was obtained by controlling the chaos of the logistic map in a variable way with the methods proposed in this work. Our results show that it is possible to simulate very complicated experimental spectra by computationally controlling the chaos of an equation unrelated to the experimental system.

Finite-Time Stabilization of Unstable Orbits in the Fractional Difference Logistic Map

“…A dynamic extended delayed feedback scheme for the control of the Rössler system is proposed in [6]. The Ott-Grebogi-York method is used to construct a computational chaos control scheme for the logistic map in [7]. Evolutionary metaheuristic methods are employed in the stabilization of the Hénon map in [8].…”