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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Applied Mathematics
- Mechanics of Materials
- Computational Mechanics