Computing and Controlling Basins of Attraction in Multistability Scenarios
Joint Authors
Taborda, John Alexander
Angulo, Fabiola
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-12-03
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Taborda, John Alexander& Angulo, Fabiola. 2015. Computing and Controlling Basins of Attraction in Multistability Scenarios. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1073493
Modern Language Association (MLA)
Taborda, John Alexander& Angulo, Fabiola. Computing and Controlling Basins of Attraction in Multistability Scenarios. Mathematical Problems in Engineering No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1073493
American Medical Association (AMA)
Taborda, John Alexander& Angulo, Fabiola. Computing and Controlling Basins of Attraction in Multistability Scenarios. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1073493
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073493