We consider a coupled dynamical system with a Milnor attractor whose basin of attraction is riddled with the basin of a second attractor. We first study how the global geometry of the basin of attraction changes as we vary the parameter in the system. Secondly, we focus on the local geometry of the riddled basin of attraction. To characterize this riddled basin, we compute a stability index for the attractor in the system. Our numerical results show that for Lebesgue almost all points in the attractor, the index is positive for some parameter region where the riddled basin occurs.
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