Abstract
A 3-D map which describes the adaptive control of a chaotic logistic equation to a fixed point is studied. Smooth and fractal regions are found in both the basin of attraction for the desired fixed point (i.e. successful control) and in the escape time pattern. These regions appear to be intertwined for the escape time pattern but for some parts of the basin boundary smooth regions appear without being intertwined with fractal regions. The existence of both smooth and fractal regions has important implications in quantifying the robustness of control algorithms which yield fractal basins.
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