Computational chaos control based on small perturbations for complex spectra simulation

Jesús Manuel Rodríguez-Núñez*, Aned de León, Martín E. Molinar-Tabares, Mario Flores-Acosta, S. J. Castillo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)835-846
Number of pages12
JournalSimulation
Volume98
Issue number9
DOIs
StatePublished - Sep 2022

Bibliographical note

Funding Information:
The financial support from Consejo Nacional de Ciencia y Tecnología (CONACyT), grant no. 351504/334851 is greatly acknowledged.

Publisher Copyright:
© The Author(s) 2022.

Keywords

  • Chaos
  • Ott–Grebogi–York method
  • computational simulation
  • control
  • logistic map

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