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 | |
| 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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Adomaitis, R. A., & Kevrekidis, I. G. (1991). Noninvertibility and the structure of basins of attraction in a model adaptive control system. Journal of Nonlinear Science, 1(1), 95-105. https://doi.org/10.1007/BF01209149