Noninvertibility and the structure of basins of attraction in a model adaptive control system

Raymond A. Adomaitis; Ioannis G. Kevrekidis

doi:10.1007/BF01209149

Noninvertibility and the structure of basins of attraction in a model adaptive control system

Raymond A. Adomaitis, Ioannis G. Kevrekidis

Chemical & Biological Engineering

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29 Scopus citations

Abstract

We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

Original language	English (US)
Pages (from-to)	95-105
Number of pages	11
Journal	Journal of Nonlinear Science
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/BF01209149
State	Published - Feb 1 1991

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Applied Mathematics
Mathematics(all)
Mechanics of Materials
Computational Mechanics

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10.1007/BF01209149

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abstract = "We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.",

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AB - We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

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Noninvertibility and the structure of basins of attraction in a model adaptive control system

Abstract

All Science Journal Classification (ASJC) codes

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