Noninvertibility and the structure of basins of attraction in a model adaptive control system |
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Authors: | Raymond A. Adomaitis Ioannis G. Kevrekidis |
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Affiliation: | (1) Department of Chemical Engineering, Princeton University, 08544 Princeton, NJ |
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Abstract: | Summary 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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Keywords: | adaptive control noninvertibility basins of attraction bifurcations |
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