Supersymmetric Multiple Basin Attractors

We explain that supersymmetric attractors in general have several critical points due to the algebraic nature of the stabilization equations. We show that the critical values of the cosmological constant of the $adS_5$ vacua are given by the topological (moduli independent) formulae analogous to the entropy of the d=5 supersymmetric black holes. We present conditions under which more than one critical point is available (for black hole entropy as well as to the cosmological constant) so that the system tends to its own locally stable attractor point. We have found several families of $Z_2$-symmetric critical points of $adS_5$ throat which may be associated with the vanishing d=4 cosmological constant.