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Mathematical Problems in Engineering
Volume 2015, Article ID 313154, 13 pages
http://dx.doi.org/10.1155/2015/313154
Research Article

Computing and Controlling Basins of Attraction in Multistability Scenarios

1Facultad de Ingeniería, Programa de Ingeniería Electrónica, Magma Ingeniería, Universidad del Magdalena, Apartado Postal 2121630, Santa Marta, Colombia
2Departamento de Ingeniería Eléctrica, Electrónica y Computación, Percepción y Control Inteligente, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia (Sede Manizales), Campus La Nubia, Bloque Q, Manizales 170003, Colombia

Received 17 October 2015; Accepted 16 November 2015

Academic Editor: Rongwei Guo

Copyright © 2015 John Alexander Taborda and Fabiola Angulo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to describe and prove a new method to compute and control the basins of attraction in multistability scenarios and guarantee monostability condition. In particular, the basins of attraction are computed only using a submap, and the coexistence of periodic solutions is controlled through fixed-point inducting control technique, which has been successfully used until now to stabilize unstable periodic orbits. In this paper, however, fixed-point inducting control is used to modify the domains of attraction when there is coexistence of attractors. In order to apply the technique, the periodic orbit whose basin of attraction will be controlled must be computed. Therefore, the fixed-point inducting control is used to stabilize one of the periodic orbits and enhance its basin of attraction. Then, using information provided by the unstable periodic orbits and basins of attractions, the minimum control effort to stabilize the target periodic orbit in all desired ranges is computed. The applicability of the proposed tools is illustrated through two different coupled logistic maps.